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	<title>Flying ThoughtsFlying Thoughts | Flying Thoughts</title>
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		<title>The Balance of Social Media</title>
		<link>http://www.michaelwillmott.com/2011/05/the-balance-of-social-media/</link>
		<comments>http://www.michaelwillmott.com/2011/05/the-balance-of-social-media/#comments</comments>
		<pubDate>Sun, 29 May 2011 18:00:15 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Film]]></category>
		<category><![CDATA[Thoughts]]></category>
		<category><![CDATA[Design]]></category>
		<category><![CDATA[Facebook]]></category>
		<category><![CDATA[Internet]]></category>
		<category><![CDATA[Social Media]]></category>
		<category><![CDATA[Spoiler]]></category>
		<category><![CDATA[systems]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.com/michael/?p=345</guid>
		<description><![CDATA[&#160; I have an interesting relationship with social media. I doubt very much i am the only one. Over the years the landscape of the virtual world has changed dramatically. Indeed, dramatic shifts in this virtual landscape have been non-stop from before i can remember. Social media is a topic of seemingly endless heated debate and discussion. This is just one more article to add to the ever expanding digital library. I hope that whilst i may not say anything new or enlightening, it will at least be of some interest to a few of you. I was spurred into writing this after having watched the film Catfish. The film is&#8230; &#8230;an American documentary involving a man being filmed by his friends as he builds a romantic relationship on the social networking website Facebook with an attractive girl, and the mysterious results when they all go to visit her. [1] This small scale, low budget film managed to catch the attention of quite a few critics a while ago with the general consensus being: &#8216;you should go and see it&#8217;. The film was short and well edited. The content was interesting and thought provoking. It wasn&#8217;t quite as gripping as [...]]]></description>
				<content:encoded><![CDATA[<p style="text-align: justify;">&nbsp;</p>
<p style="text-align: justify;">I have an interesting relationship with social media. I doubt very much i am the only one. Over the years the landscape of the virtual world has changed dramatically. Indeed, dramatic shifts in this virtual landscape have been non-stop from before i can remember. Social media is a topic of seemingly endless heated debate and discussion. This is just one more article to add to the ever expanding digital library. I hope that whilst i may not say anything new or enlightening, it will at least be of some interest to a few of you.</p>
<p style="text-align: justify;">I was spurred into writing this after having watched the film <em><a href="http://www.imdb.com/title/tt1584016/" target="_blank">Catfish</a>. </em>The film is&#8230;</p>
<blockquote><p><em><strong> </strong></em> &#8230;an American documentary involving a man being filmed by his friends as he builds a romantic relationship on the social networking website Facebook with an attractive girl, and the mysterious results when they all go to visit her. <sup id="cite-ref-1"><a href="#ref-1">[1]</a></sup></p></blockquote>
<div class="wp-caption alignright" style="width: 160px"><img class=" " title="Catfish (Film)" src="http://upload.wikimedia.org/wikipedia/en/7/73/Catfish_film.jpg" alt="Catfish (Film)" width="150" /><p class="wp-caption-text"> </p></div>
<p style="text-align: justify;">This small scale, low budget film managed to catch the attention of quite a few critics a while ago with the general consensus being: &#8216;you should go and see it&#8217;. The film was short and well edited. The content was interesting and thought provoking. It wasn&#8217;t quite as gripping as i was led to expect and the twist was a slight let down. There has been much speculation on the authenticity of the film and whether or not the whole thing is staged. Personally, i don&#8217;t care either way. The film got me to engage in a discussion on it and the wider premise of social media. It feels to me as though this was the intention of the film all along. If it is staged then the directors have done a convincing job and i would certainly see something by them again.</p>
<p style="text-align: justify;">So at this point i should issue a <strong>spoiler alert</strong>. I am about to reveal the twist in the film (to a degree) and whilst i don&#8217;t feel that this is any great revelation i should probably warn you anyway.</p>
<p style="text-align: justify;">The main character (one of the film makers) is drawn into a friendship with a family that live on the other side of the USA. He develops deep emotional relationships with these people even though he has never met them before. The crux of the story is (obviously) that these people are not who they seem to be. In fact all of these online personalities are products of one woman&#8217;s imagination. She is ultimately found out and the whole story unravels in quite an emotional and touching way. The gentle unravelling actually lends itself to making the whole situation more sinister than it might otherwise be.</p>
<p style="text-align: justify;">This is the point for me when the questions started to brew and the thinking began. I feel that this is a deeply disturbing situation with a worrying undertone to it. A woman has invented personalities within the virtual world, and managed to weave them into a real persons life. So for me this is an extreme case, but when i begin to think about how others interact with social media then i find the line which separates an unsettling invasion of ones personal life and one of normal social interaction becomes blurred. This blurred line leads me to ask the following questions:</p>
<blockquote><p>How are we as affected by the now intrinsic links we have developed with/using social media?</p>
<p>To what extent are real life relationships manipulated or shaped by social media?</p></blockquote>
<h5>The Evolution of Social Media</h5>
<p>So let us first look at the way that social media has evolved to become such an integral part of modern society. In June 2009 Social Media Rockstar posted an article that began:</p>
<blockquote><p>Social media isn’t really  “new.” While it has only recently become part of mainstream culture and  the business world,  people have been using digital media for  networking, socializing and information gathering – almost exactly like  now – <em>for over 30 years</em>. <sup id="cite-ref-1"><a href="#ref-2">[2]</a></sup></p></blockquote>
<p style="text-align: justify;">It could be argued that modern social media came about when people began to understand the potential of the telephone network. Then along came the internet and the social media phenomenon really kicked off. It certainly took a while (relative to the life of the internet) for social media to reach the masses though. It all began with methods of communication that were limited and a tad difficult to use. Usernet, Internet Relay Chat (which eventually let to instant messaging) and online forums were only really used by the bright sparks that understood it all. The foundations for social media existed and were accessible in the sense that almost anyone could plug in. The great leap that led to the social media dominated environment we know today was making it easy for anyone to access and interact with.</p>
<p style="text-align: justify;">There were some key players that led this social media revolution. People and companies that understood how to design a service, not sell a technology (even if they developed the technology). The first sites to really tap into this were essentially dating sites. They saw that people wanted to connect with each other. They understood that people would want to try and develop a relationship in ways they were used to. So the task was to enable this and ensure that the virtual middleman didn&#8217;t make the process seem to disconnected. How did they do this? Firstly through good design. They made their service easy to use. Secondly, they invited the user to put as much information about themselves on the internet as possible. If it wasn&#8217;t going to be possible to interact with the real person then give the feeling of interaction by letting them know about you. Of course, by today&#8217;s standards the information they would have uploaded was minimal. The amount of information we are willing to divulge has been growing as social media has evolved.</p>
<p style="text-align: justify;">At the same the world of online forums began to evolve. There is an important distinction to make here because the use of the word forum implies that it is simply a place for discussion. Whilst this is true, there have been places for discussion almost from the beginning of the web. The internet was, after all, created to connect a very specific groups of people. They existed purely as a means of communication, originally to transfer data, but soon after to transfer communicate. When we talk about online forums we now mean communities based on discussion. The great step that was taken here was to open up these communities and make it much easier for anyone to get involved. Forums were springing up all over the place, communities of people with specific interests who could communicate with one another. This was the state of the web until the late 90&#8242;s. It was at this point that the really big changes came about.</p>
<p style="text-align: justify;">The development of the internet was happening at a staggering rate. More and more people were connecting and more and more content was being added by its users. This was in the days before search engines as we know them, before people really appreciated the need for an organised web. The web was for want of a better word, disjointed. The successive moves to organise content and connect people to it and each other is what led to the development of social media as we now know it. This framework, with an increased and ever developing understanding of  how people interact with each other and content led to the behemoths that now stand tall in the social  media landscape (or in a pile of ruins as is the case for some).</p>
<p>Social media is a creation driven by our own desire to connect and share. Companies like Facebook, Twitter and Google have merely understood how to bring us together through a new medium. Their commercial success has resulted from their understanding of how to use the information we hand over (or even unwittingly generate such as when we search using Google, or form connections using Facebook).</p>
<h5>But all of this is great! What&#8217;s your point?</h5>
<p>It is all to do with motivation. Social media both exists and thrives on the motivations of the general consumers, those that fund it, content creators and those that wish to benefit from our use of it. The problem arises when we ask whether we understand the motivations of all the different stakeholders? It is quite simple when i look at the connection between myself and a school friend on Facebook; we want to stay in touch. We want to share information about ourselves with each other. But, going back to the film, what about the connection between the film maker and the imaginary personalities? How do his motivations align with those of the actual person behind the fake profiles? You can extend this train of thought indefinitely, looking at the connections people have with advertisers, the companies that run the sites we use, the people that connect to us indirectly. Even between a reader and someone who blogs with a political bias.</p>
<p>As soon as one starts to appreciate the scale of how we connect to others through social media, you realise that maybe our motivations for sharing information aren&#8217;t aligned with those of other stakeholders in a way we were expecting. However, because we are forming these connections we are at least subject to the motivations of others. For example, because i chose to share information about myself in order to connect with a friend I am now connected to an advertiser who knows more about me than ever. This probably influences my &#8220;real life&#8221; connection (or my perception of the connection I have) with a product/brand quite a lot.</p>
<p>Now I&#8217;m not saying this is all a terrible thing. I am in awe of how social media has evolved and generally consider it to be a triumph of the internet. I would say that in general the way companies use information about me to target adverts and to highlight things that might be of interest to me is a good thing. The message I would like to leave you with though is that the power of social media to influence us shouldn&#8217;t be underestimated. On the internet anonymity is easier than authenticity and this is something I feel we are all to happy to forget. It is for good reason that issues of privacy are hot topics of discussion at the moment. Just as a last point, the next time you click &#8216;Like&#8217; to a post or you find that someone you don&#8217;t know is following you on Twitter think about what connection you have just formed, and who the person on the other end might be.</p>
<ol>
<li id="ref-1"><a href="http://en.wikipedia.org/wiki/Catfish_(film)" target="_blank">http://en.wikipedia.org/wiki/Catfish_(film)</a> Retrieved 22/12/2010</li>
<li id="ref-2"><a href="http://socialmediarockstar.com/history-of-social-media" target="_blank">http://socialmediarockstar.com/history-of-social-media</a> Retrieved 22/12/2010</li>
</ol>
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		<title>Designing a Solution to Medication Compliance?</title>
		<link>http://www.michaelwillmott.com/2010/11/designing-a-solution-to-medication-compliance/</link>
		<comments>http://www.michaelwillmott.com/2010/11/designing-a-solution-to-medication-compliance/#comments</comments>
		<pubDate>Mon, 22 Nov 2010 22:28:05 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Design]]></category>
		<category><![CDATA[Education]]></category>
		<category><![CDATA[Design London]]></category>
		<category><![CDATA[get involved]]></category>
		<category><![CDATA[Medication Compliance]]></category>
		<category><![CDATA[Project Work]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.com/michael/?p=283</guid>
		<description><![CDATA[This year i started on the Design-led Innovation and New Venture Creation course run by Design London. Design London is a joint venture between Imperial College London (where i am currently studying) and the Royal College of Art. Design London develops, teaches, researches and delivers radical new practices, tools and processes that transform the way organisations innovate, and helps them translate their creativity into commercial success. I think this course is brilliant! I have classmates that disagree and i will write a longer post at a later date talking more about what i&#8217;m learning. In this post i wanted to talk about our project and hopefully get some sort of discussion going. As a team we are looking into the issue of medication compliance within the NHS. Approximately £7.6 billion is spent on prescription drugs each year by the NHS. It is estimated that up to 40% of the drugs given out are wasted. This is clearly a huge source of wastage for the NHS with the biggest blow being felt in the finances. Medication non-compliance can also have huge repercussions for the NHS with an increase in hospital admissions. The issue of compliance is a complicated one and something that [...]]]></description>
				<content:encoded><![CDATA[<p>This year i started on the Design-led Innovation and New Venture Creation course run by <a href="http://www.designlondon.net/" target="_blank">Design London</a>. Design London is a joint venture between Imperial College London (where i am currently studying) and the Royal College of Art.</p>
<blockquote><p>Design London develops, teaches, researches and delivers radical new practices, tools and processes that transform the way organisations innovate, and helps them translate their creativity into commercial success.</p></blockquote>
<p>I think this course is brilliant! I have classmates that disagree and i will write a longer post at a later date talking more about what i&#8217;m learning. In this post i wanted to talk about our project and hopefully get some sort of discussion going.</p>
<p>As a team we are looking into the issue of medication compliance within the NHS. Approximately £7.6 billion is spent on prescription drugs each year by the NHS. It is estimated that up to 40% of the drugs given out are wasted. This is clearly a huge source of wastage for the NHS with the biggest blow being felt in the finances. Medication non-compliance can also have huge repercussions for the NHS with an increase in hospital admissions. The issue of compliance is a complicated one and something that is being looked into in increasing detail. The reasons for non-compliance vary hugely and so it may seem like a daunting task.</p>
<p><strong>So where does &#8216;design&#8217; fit into this? </strong>We are looking at developing a solution to this issue that takes into account technical, socio-cultural and economic factors. The brief is simple but broad. It is unlikely that there exists one uniform solution to the problem (and if there were it would almost certainly be heavily routed in process and systems design). If we can come up with something that helps tackle issues of compliance in one small area then brilliant! If someone else can tackle another area then thats two down. It may well be that there are some big grand ideas out there. I certainly have a few. Whether they will work or not is a completely different question.</p>
<p>So hopefully that is enough of an introduction to what i am doing. I haven&#8217;t been very structured in my approach but it will do for now! I want need help from you, the reader. There are so many people out there that know so much more than me and i can bring just a few of your minds together and throw in some creative input from others i think we can pull something brilliant out of the mix.</p>
<p><strong>So for discussion:</strong></p>
<ul>
<li>The general question: what are your views on the issue of medication compliance?</li>
<li>Have you ever been in, or can imagine a situation whereby you are forgetting to take medication? What is the medication? What does it help you with? Why do you forget to take it?</li>
<li>When you visit the doctor and receive a prescription, do you ever feel like somehow this could be better? Be it the packaging the medication comes in, being educated by your doctor etc.</li>
<li>Why might people not take their medication?</li>
</ul>
<p>Drawing on personal experience is brilliant. Speculation is good but can often lead to developing solutions to problems that we have convinced ourselves of&#8230; but don&#8217;t actually exists. I realise this could possibly be a sensitive issue so please feel free to be annonomous in the comments or just send me and email so we can discuss it in private.</p>
<p>Thank you in advance. I am looking forward to this! Please get anyone else you know involved!</p>
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		<title>Welcome to the USA&#8230; now empty your bag</title>
		<link>http://www.michaelwillmott.com/2010/07/welcome-to-the-usa-now-empty-your-bag/</link>
		<comments>http://www.michaelwillmott.com/2010/07/welcome-to-the-usa-now-empty-your-bag/#comments</comments>
		<pubDate>Fri, 09 Jul 2010 14:24:59 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Travel]]></category>
		<category><![CDATA[Boston]]></category>
		<category><![CDATA[Flying]]></category>
		<category><![CDATA[USA]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.com/michael/?p=274</guid>
		<description><![CDATA[So firstly, the websites a bit of a mess. It&#8217;s not finished and i probably won&#8217;t be doing much to it whilst away, but nevermind. It also turns out that i don&#8217;t have wifi in the hostel so might not be online as much as i thought. I am currently in Borders across the road from Boston Public Library. Got up at 7am to have breakfast and decided to travel into town for it. Well then, i am in Boston! I have started my 3 week trip to the USA and will hopefully be writing about my trip on a regular basis. I have to take lots of photos to bore people with because i bought myself a new camera especially for this trip. So the trip here went pretty. I have honestly never had such brilliant food on a plane! I can honestly say it was delicious. The plane was also fairly empty which was nice, i didn&#8217;t have anyone sitting next to me so the journey was nice and comfortable. The entertainment system was&#8230; entertaining. It didn&#8217;t work, it seemed to throw a bit of fit and, sitting at the back of the plane, i could watch each [...]]]></description>
				<content:encoded><![CDATA[<p>So firstly, the websites a bit of a mess. It&#8217;s not finished and i probably won&#8217;t be doing much to it whilst away, but nevermind. It also turns out that i don&#8217;t have wifi in the hostel so might not be online as much as i thought. I am currently in Borders across the road from Boston Public Library. Got up at 7am to have breakfast and decided to travel into town for it.</p>
<p>
<a href="http://www.michaelwillmott.com/wp-gallery/boston-2010/DSC00020.JPG" title="" class="highslide" onclick="return hs.expand(this, { slideshowGroup: 'singlepic20' })" >
	<img class="ngg-singlepic ngg-left" src="http://www.michaelwillmott.com/wp-gallery/cache/20__320x240_DSC00020.JPG" alt="DSC00020" title="DSC00020" />
</a>
Well then, i am in Boston! I have started my 3 week trip to the USA and will hopefully be writing about my trip on a regular basis. I have to take lots of photos to bore people with because i bought myself a new camera especially for this trip. So the trip here went pretty. I have honestly never had such brilliant food on a plane! I can honestly say it was delicious. The plane was also fairly empty which was nice, i didn&#8217;t have anyone sitting next to me so the journey was nice and comfortable. The entertainment system was&#8230; entertaining. It didn&#8217;t work, it seemed to throw a bit of fit and, sitting at the back of the plane, i could watch each persons screen fail in succession. It didn&#8217;t matter though, BA were &#8211; as expected &#8211; very good. I even got a small bottle of wine with my meal!</p>
<p>Arriving was interesting,  i had no idea how completely paranoid the Americans have become about letting people into the country. I can see that i might be slightly suspicious: a student travelling on his own to a major US city even though he has no friends or family there. Leaving the US from a different city. But seriously, it was like the Spanish inquisition! The amount of information they now have stored on their systems about me is rediculous, right down to the exact amount of money i had on me when entering the US. It wasn&#8217;t really a problem though, i left the airport and managed to get to the hostel in no time at all (mostly by luck seen as i jumped on a train and a bus without being completely sure where it was going).</p>
<p>So i arrived in Boston at about 3pm Eastern time. I have been given a room with 3 beds in and an ensuite shower. It is just a dorm room in Boston University Halls. When i arrived there was nobody else in the room which was slightly disappointing.</p>

<a href="http://www.michaelwillmott.com/wp-gallery/boston-2010/DSC00023.JPG" title="" class="highslide" onclick="return hs.expand(this, { slideshowGroup: 'singlepic21' })" >
	<img class="ngg-singlepic ngg-center" src="http://www.michaelwillmott.com/wp-gallery/cache/21__650x_DSC00023.JPG" alt="DSC00023" title="DSC00023" />
</a>

<p>After a quick shower i decided to do the standard thing (for anyone who isn&#8217;t American) and go for a long walk around the area. First thoughts are that Boston is a bit of a strange place, but i really like it. I can&#8217;t quite put my finger on it but it feels like it is trying to be bigger than it actually is. I took a walk downtown towards the Prudential Centre. It&#8217;s quite a spectacular area and seen as i really didn&#8217;t feel like being in a restaurant i decided to go to a Wendy&#8217;s for the first time in about 8 years, grabbed a burger and sat outside to eat and watch Boston go by.</p>
<p>I headed back to the hostel to grab some sleep ready for the next day. Discovered that whilst i had been away two people had moved into the room. I am now living with a guy from Paris who has been working in Toronto and is on his way to Brazil (still not quite sure why he is in Boston), and a guy from Portugal&#8230; i think. I also got talking to some people downstairs in the lounge, a guy from California and a girl from Brazil. We are meeting up later today to go wondering around Boston on some walking tour.</p>
<p>On that note, i had probably better go and make use of the day!</p>
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		<title>I love Higher Education!</title>
		<link>http://www.michaelwillmott.com/2010/04/i-love-higher-education/</link>
		<comments>http://www.michaelwillmott.com/2010/04/i-love-higher-education/#comments</comments>
		<pubDate>Tue, 06 Apr 2010 22:49:53 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Education]]></category>
		<category><![CDATA[get involved]]></category>
		<category><![CDATA[Hair]]></category>
		<category><![CDATA[lovehecampaign]]></category>
		<category><![CDATA[New Blog]]></category>
		<category><![CDATA[SAC]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.com/michael/?p=249</guid>
		<description><![CDATA[Hello! Well, it has been almost a year exactly since I last posted here. This blog just never really kicked off&#8230; I have spent the last year wanting to write something on here but never really got around to it. Anyway, I intend to start doing so in earnest. Also, the website is in a complete mess at the moment. I haven&#8217;t finished it but wanted to stick the little I had done online. Bear with me whilst I finish it, you can even give me feedback if you so wish. So, a few weeks ago I was sitting in the Student Activities Centre at ICU. I was trying to get a lab write-up on Boundary Layers written. The week was a crazy one as it was the week I was performing in Hair and hence I was fitting in work wherever I could. Hair by the way, was the most incredible experience of my life. People often say this about events in their life but I genuinely believe it to be true. I am veering off topic. So suddenly these two reporters from The Times Higher Education come in and proceed to go and meet with our DPCS. A [...]]]></description>
				<content:encoded><![CDATA[<p>Hello!</p>
<p>Well, it has been almost a year exactly since I last posted here. This blog just never really kicked off&#8230; I have spent the last year wanting to write something on here but never really got around to it. Anyway, I intend to start doing so in earnest. Also, the website is in a complete mess at the moment. I haven&#8217;t finished it but wanted to stick the little I had done online. Bear with me whilst I finish it, you can even give me feedback if you so wish.</p>
<p>So, a few weeks ago I was sitting in the Student Activities Centre at ICU. I was trying to get a lab write-up on Boundary Layers written. The week was a crazy one as it was the week I was performing in Hair and hence I was fitting in work wherever I could. Hair by the way, was the most incredible experience of my life. People often say this about events in their life but I genuinely believe it to be true. I am veering off topic.</p>
<p>So suddenly these two reporters from The Times Higher Education come in and proceed to go and meet with our DPCS. A few moments later our DPCS appears and plucks the people whose names she knows to go and tell the reporters why they love Higher Education. Those picked received a lovely flash pen (they were going to give us cake but it all &#8220;mysteriously vanished in the office&#8221;) and yes, I was one of those lucky people. So, here I am on YouTube saying why I love HE!</p>
<p><object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" width="480" height="385" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="allowFullScreen" value="true" /><param name="allowscriptaccess" value="always" /><param name="src" value="http://www.youtube.com/v/gGHUc27kpPE&amp;hl=en_GB&amp;fs=1&amp;" /><param name="allowfullscreen" value="true" /><embed type="application/x-shockwave-flash" width="480" height="385" src="http://www.youtube.com/v/gGHUc27kpPE&amp;hl=en_GB&amp;fs=1&amp;" allowscriptaccess="always" allowfullscreen="true"></embed></object></p>
<p>You can find out more about the <a href="http://www.timeshighereducation.co.uk/lovehe" target="_blank">LoveHEcampaign </a>on the Times Higher Education website.</p>
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		<title>The Discrete-Time Convolution Sum</title>
		<link>http://www.michaelwillmott.com/2009/05/the-discrete-time-convolution-sum/</link>
		<comments>http://www.michaelwillmott.com/2009/05/the-discrete-time-convolution-sum/#comments</comments>
		<pubDate>Wed, 13 May 2009 21:31:55 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Engineering]]></category>
		<category><![CDATA[Question]]></category>
		<category><![CDATA[maths]]></category>
		<category><![CDATA[signals]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=183</guid>
		<description><![CDATA[Suppose we have the following two signals: The convolution sum is as follows: Now the problem: I think that for : This does not lead to the given solution: How does one get to the given solution and how is mine wrong?]]></description>
				<content:encoded><![CDATA[<p>Suppose we have the following two signals:</p>
<div style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=x%5Bn%5D%3D%5Cbegin%7Bcases%7D%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5En%20%26%20n%20%5Cge%200%20%5C%5C%200%20%26%20%5Cmbox%7Botherwise%7D%20%5Cend%7Bcases%7D%20%5Cmbox%7B%20and%20%7D%20h%5Bn%5D%3D%5Cbegin%7Bcases%7D-1%20%26%200%20%5Cle%20n%20%5Cle%2010%20%5C%5C%200%20%26%20%5Cmbox%7Botherwise%7D%20%5Cend%7Bcases%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='x[n]=\begin{cases}\left ( \frac{1}{3} \right )^n &amp; n \ge 0 \\ 0 &amp; \mbox{otherwise} \end{cases} \mbox{ and } h[n]=\begin{cases}-1 &amp; 0 \le n \le 10 \\ 0 &amp; \mbox{otherwise} \end{cases}' title='x[n]=\begin{cases}\left ( \frac{1}{3} \right )^n &amp; n \ge 0 \\ 0 &amp; \mbox{otherwise} \end{cases} \mbox{ and } h[n]=\begin{cases}-1 &amp; 0 \le n \le 10 \\ 0 &amp; \mbox{otherwise} \end{cases}' class='latex' /></div>
<p>The convolution sum <img src='http://s.wordpress.com/latex.php?latex=y%5Bn%5D%3Dx%5Bn%5D%2Ah%5Bn%5D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='y[n]=x[n]*h[n]' title='y[n]=x[n]*h[n]' class='latex' /> is as follows:</p>
<div style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=y%5Bn%5D%3D%5Cbegin%7Bcases%7D0%20%26%20%5Cmbox%7Bif%20%7D%20n%3C0%20%5C%5C%20%5Cfrac%7B-1%2B%20%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5E%7Bn%2B1%7D%7D%7B1-%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%7D%20%26%20%5Cmbox%7Bif%20%7D%200%20%5Cle%20n%20%5Cle%2010%20%5C%5C%20%3F%20%26%20%5Cmbox%7Bif%20%7Dn%20%5Cge%2011%20%5Cend%7Bcases%7D&#038;bg=ffffff&#038;fg=000000&#038;s=1' alt='y[n]=\begin{cases}0 &amp; \mbox{if } n&lt;0 \\ \frac{-1+ \left ( \frac{1}{3} \right )^{n+1}}{1-\left ( \frac{1}{3} \right )} &amp; \mbox{if } 0 \le n \le 10 \\ ? &amp; \mbox{if }n \ge 11 \end{cases}' title='y[n]=\begin{cases}0 &amp; \mbox{if } n&lt;0 \\ \frac{-1+ \left ( \frac{1}{3} \right )^{n+1}}{1-\left ( \frac{1}{3} \right )} &amp; \mbox{if } 0 \le n \le 10 \\ ? &amp; \mbox{if }n \ge 11 \end{cases}' class='latex' /></div>
<p>Now the problem: I think that for <img src='http://s.wordpress.com/latex.php?latex=n%20%5Cge%2011&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n \ge 11' title='n \ge 11' class='latex' />:</p>
<div style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=y%5Bn%5D%3D-%5Cdisplaystyle%5Csum_%7Bk%3Dn-10%7D%5En%20%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5Ek&#038;bg=ffffff&#038;fg=000000&#038;s=1' alt='y[n]=-\displaystyle\sum_{k=n-10}^n \left ( \frac{1}{3} \right )^k' title='y[n]=-\displaystyle\sum_{k=n-10}^n \left ( \frac{1}{3} \right )^k' class='latex' /></div>
<p>This does not lead to the given solution:</p>
<div style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=y%5Bn%5D%3D%5Cleft%20%28%20%5Cfrac%7B-1%2B%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5E%7B11%7D%7D%7B1-%5Cfrac%7B1%7D%7B3%7D%7D%20%5Cright%20%29%20%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5E%7Bn-11%7D&#038;bg=ffffff&#038;fg=000000&#038;s=1' alt='y[n]=\left ( \frac{-1+\left ( \frac{1}{3} \right )^{11}}{1-\frac{1}{3}} \right ) \left ( \frac{1}{3} \right )^{n-11}' title='y[n]=\left ( \frac{-1+\left ( \frac{1}{3} \right )^{11}}{1-\frac{1}{3}} \right ) \left ( \frac{1}{3} \right )^{n-11}' class='latex' /></div>
<p>How does one get to the given solution and how is mine wrong?</p>
]]></content:encoded>
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		<item>
		<title>Confusion over System Properties</title>
		<link>http://www.michaelwillmott.com/2009/05/confusion-over-system-properties/</link>
		<comments>http://www.michaelwillmott.com/2009/05/confusion-over-system-properties/#comments</comments>
		<pubDate>Sun, 10 May 2009 16:16:59 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Question]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=168</guid>
		<description><![CDATA[We have the following system: Where is an input (not neccessarily the unit step, great notation!) and is the output and is a complex number. According to the tutorial answers this system is nether time-invariant, linear or stable. I thought it was all of these as well as memoryless and causal! Am i actually wrong and if so why? Also, consider the following system: Is this system unstable? I imagine it depends entirely on the signal , for example, if then a bounded input produces an unbounded output? Any help would be greatly appreciated!]]></description>
				<content:encoded><![CDATA[<p>We have the following system:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=y%28t%29%20%3D%20Ku%28t%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='y(t) = Ku(t)' title='y(t) = Ku(t)' class='latex' /></p>
<p>Where <img src='http://s.wordpress.com/latex.php?latex=u%28t%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='u(t)' title='u(t)' class='latex' /> is an input (not neccessarily the unit step, great notation!) and <img src='http://s.wordpress.com/latex.php?latex=y%28t%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='y(t)' title='y(t)' class='latex' /> is the output and <img src='http://s.wordpress.com/latex.php?latex=K&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='K' title='K' class='latex' /> is a complex number.</p>
<p>According to the tutorial answers this system is nether time-invariant, linear or stable. I thought it was all of these as well as memoryless and causal! Am i actually wrong and if so why?</p>
<p>Also, consider the following system:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=y%28t%29%3D%20%5Cint_%7B-%5Cinfty%7D%5E%7B2t%7D%20u%28%5Ctau%29%5C%2C%20d%5Ctau&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='y(t)= \int_{-\infty}^{2t} u(\tau)\, d\tau' title='y(t)= \int_{-\infty}^{2t} u(\tau)\, d\tau' class='latex' /></p>
<p>Is this system unstable? I imagine it depends entirely on the signal <img src='http://s.wordpress.com/latex.php?latex=u%28%5Ctau%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='u(\tau)' title='u(\tau)' class='latex' />, for example, if <img src='http://s.wordpress.com/latex.php?latex=u%28%5Ctau%29%3D%5Ctau&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='u(\tau)=\tau' title='u(\tau)=\tau' class='latex' /> then a bounded input produces an unbounded output?</p>
<p>Any help would be greatly appreciated!</p>
]]></content:encoded>
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		<title>Periodicity Properties of Discrete and Continuous Time Complex Exponentials</title>
		<link>http://www.michaelwillmott.com/2009/05/periodicity-properties-of-discrete-and-continuous-time-complex-exponentials/</link>
		<comments>http://www.michaelwillmott.com/2009/05/periodicity-properties-of-discrete-and-continuous-time-complex-exponentials/#comments</comments>
		<pubDate>Mon, 04 May 2009 14:20:58 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Question]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=150</guid>
		<description><![CDATA[A continuous time complex exponential, , has the following properties: The larger the magnitude of , the higher the rate of oscillation in the signal. is periodic for any value of . However, for a discrete time complex exponential, , the exponential at frequency is the same as that at frequency . This means that as we increase from 0, we obtain signals that oscillate more and more rapidly until we reach . As we continue to increase we decrease the rate of oscillation until we reach . This shows that for discrete time the first property is different to that in continuous time. My question is, why mathematically are the two properties different? Why when you vary between 0 and is the rate of oscillation different for the two cases?]]></description>
				<content:encoded><![CDATA[<p>A continuous time complex exponential, <img src='http://s.wordpress.com/latex.php?latex=%20e%5E%7Bj%20%5Comega_o%20t%7D%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' e^{j \omega_o t} ' title=' e^{j \omega_o t} ' class='latex' />, has the following properties:</p>
<ol>
<li>The larger the magnitude of <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' />, the higher the rate of oscillation in the signal.</li>
<li><img src='http://s.wordpress.com/latex.php?latex=%20e%5E%7Bj%20%5Comega_o%20t%7D%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' e^{j \omega_o t} ' title=' e^{j \omega_o t} ' class='latex' /> is periodic for any value of <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' />.</li>
</ol>
<p>However, for a discrete time complex exponential, <img src='http://s.wordpress.com/latex.php?latex=%20e%5E%7Bj%20%5Comega_o%20n%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' e^{j \omega_o n}' title=' e^{j \omega_o n}' class='latex' />, the exponential at frequency <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o%20%2B%202%5Cpi&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o + 2\pi' title='\omega_o + 2\pi' class='latex' /> is the same as that at frequency <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' />. This means that as we increase <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' /> from 0, we obtain signals that oscillate more and more rapidly until we reach <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o%20%3D%20%5Cpi&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o = \pi' title='\omega_o = \pi' class='latex' />. As we continue to increase <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' /> we decrease the rate of oscillation until we reach <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o%20%3D%202%5Cpi&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o = 2\pi' title='\omega_o = 2\pi' class='latex' />. This shows that for discrete time the first property is different to that in continuous time.</p>
<p>My question is, why mathematically are the two properties different? Why when you vary <img src='http://s.wordpress.com/latex.php?latex=%5Comega_o&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\omega_o' title='\omega_o' class='latex' /> between 0 and <img src='http://s.wordpress.com/latex.php?latex=2%5Cpi&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='2\pi' title='2\pi' class='latex' /> is the rate of oscillation different for the two cases?</p>
]]></content:encoded>
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		<title>Mixed Signals</title>
		<link>http://www.michaelwillmott.com/2009/04/mixed-signals/</link>
		<comments>http://www.michaelwillmott.com/2009/04/mixed-signals/#comments</comments>
		<pubDate>Mon, 06 Apr 2009 23:19:51 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Computing]]></category>
		<category><![CDATA[Engineering]]></category>
		<category><![CDATA[matlab]]></category>
		<category><![CDATA[numerical methods]]></category>
		<category><![CDATA[propulsion]]></category>
		<category><![CDATA[signals]]></category>
		<category><![CDATA[systems]]></category>
		<category><![CDATA[turbomachinery]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=133</guid>
		<description><![CDATA[Now the title for this post would imply that the content is much more interesting than it is likely to be, at least, that is how i would take it. I am disappointed by the content already and i haven&#8217;t written it. I suppose that is largely due to the fact that i have nothing much to write about. My day has been very disjointed. It has been moderately productive but i keep switching and not sticking with things. I started off by going over my Propulsion and Turbomachinery module. Fairly interesting. I was motivated to really get to grips with this when i visited Rolls-Royce in Derby a month or so ago. I was having a look around their precision casting facility where they make the turbine blades for jet engines. Also went into their new maintenance plant for their jet engines. It was incredible and reminded me of why i want to be an engineer. I had a brief period of thinking that banking looked ok, glad i have gone through that phase none the worse. Anyway, that motivation i managed to acquire from RR seems to have been misplaced and i couldn&#8217;t continue with it. I switched [...]]]></description>
				<content:encoded><![CDATA[<p>Now the title for this post would imply that the content is much more interesting than it is likely to be, at least, that is how i would take it. I am disappointed by the content already and i haven&#8217;t written it. I suppose that is largely due to the fact that i have nothing much to write about. My day has been very disjointed. It has been moderately productive but i keep switching and not sticking with things.</p>
<p>I started off by going over my Propulsion and Turbomachinery module. Fairly interesting. I was motivated to really get to grips with this when i visited Rolls-Royce in Derby a month or so ago. I was having a look around their precision casting facility where they make the turbine blades for jet engines. Also went into their new maintenance plant for their jet engines. It was incredible and reminded me of why i want to be an engineer. I had a brief period of thinking that banking looked ok, glad i have gone through that phase none the worse.</p>
<p>Anyway, that motivation i managed to acquire from RR seems to have been misplaced and i couldn&#8217;t continue with it. I switched to what i have decided is my favourite of subjects, signals and systems. I find the whole area both enjoyable (weird considering it is mostly Fourer Transforms) and interesting. It just brings together so many concepts i have previously learnt and thought to be useless and apply them to really interesting real life situations. For instance, it was shown to be through the use of signal processing that if, for instance, you are cycling along or flying a plane in a straight line, if you adjust the handle bars or flight controls to move the bike or plane to the right (assuming in the case of the bike your body is directly above the frame and you do not shift your weight) the bike/plane will actually turn to the left shortly and then swing to the right. This blip is hardly noticeable but it happens! That is incredible. I tried this when cycling home, turns out it is rather difficult and i quite dangerous when on the busy streets of London.</p>
<p>Here is a question. I was going back over the basics and the book i was reading said that an odd signal by definition had to have an amplitude of 0 at the origin. Is it not possible to have a signal with a discontinuity at 0 though, thereby meaning that the amplitude of the signal will not be 0?</p>
<p>Anyway, i have since been writing a Matlab program to solve a one dimensional unsteady heat conduction in a multi-layered bar. Very happy as i am getting it. I am amazed at how through the use of numerical methods a problem seemingly complicated can be solved with such a, dare i say it, beautiful solution. Initially i expected such a task to be horrific but not so!</p>
<p>Anyway, i am rambling and it is no doubt boring. I found something to write about at any rate. I shall have to write something less geeky soon to balance this blog out.</p>
<p>Good Night!</p>
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		<title>The Problem!</title>
		<link>http://www.michaelwillmott.com/2009/04/the-problem/</link>
		<comments>http://www.michaelwillmott.com/2009/04/the-problem/#comments</comments>
		<pubDate>Sun, 05 Apr 2009 22:07:46 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>
		<category><![CDATA[circuits]]></category>
		<category><![CDATA[ill]]></category>
		<category><![CDATA[signals]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=38</guid>
		<description><![CDATA[Evening, My second post! This has taken me much longer to do than i would have liked but nevermind. I would like to say that it is because i have been wonderfully productive and as such have not had the time to post but that would not be the entire truth. My work is not going as well as it should and i have been feeling rotten for quite a few days now. I have got my first technical post saved as a draft but i don&#8217;t quite understand what i am writing about. I am trying to come to grips with the response of a first order circuit when the input is a unit step (below). Infact, i have probably worded that incorrectly. If anyone knows about this stuff please do help. I will post a more specific plea for help if i still don&#8217;t get it by tomorrow. Anyway, it is getting late and i want to go to bed. Hopefully the gap until the next post won&#8217;t be quite so long!]]></description>
				<content:encoded><![CDATA[<p>Evening,</p>
<p>My second post! This has taken me much longer to do than i would have liked but nevermind. I would like to say that it is because i have been wonderfully productive and as such have not had the time to post but that would not be the entire truth. My work is not going as well as it should and i have been feeling rotten for quite a few days now.</p>
<p>I have got my first technical post saved as a draft but i don&#8217;t quite understand what i am writing about. I am trying to come to grips with the response of a first order circuit when the input is a unit step (below).</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=u%28t%20-%20t_0%29%20%3D%20%5Cbegin%7Bcases%7D%200%2C%20%26%20%5Cmbox%7Bt%7D%20%3C%20t_0%20%5C%5C%201%2C%20%26%20%5Cmbox%7Bt%7D%20%3E%20t_0%20%5Cend%7Bcases%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='u(t - t_0) = \begin{cases} 0, &amp; \mbox{t} &lt; t_0 \\ 1, &amp; \mbox{t} &gt; t_0 \end{cases}' title='u(t - t_0) = \begin{cases} 0, &amp; \mbox{t} &lt; t_0 \\ 1, &amp; \mbox{t} &gt; t_0 \end{cases}' class='latex' /></p>
<p>Infact, i have probably worded that incorrectly. If anyone knows about this stuff please do help. I will post a more specific plea for help if i still don&#8217;t get it by tomorrow.</p>
<p>Anyway, it is getting late and i want to go to bed. Hopefully the gap until the next post won&#8217;t be quite so long!</p>
]]></content:encoded>
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		<title>The Beginning</title>
		<link>http://www.michaelwillmott.com/2009/03/the-beginning/</link>
		<comments>http://www.michaelwillmott.com/2009/03/the-beginning/#comments</comments>
		<pubDate>Mon, 30 Mar 2009 23:05:03 +0000</pubDate>
		<dc:creator>Michael Willmott</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>

		<guid isPermaLink="false">http://www.the-willmotts.co.uk/michael/?p=36</guid>
		<description><![CDATA[Well, my first blog post. This has taken me ages to do. I have wanted a blog for quite a while now but never got around to setting it up. It shouldn&#8217;t take ages but i run this on my own web servers and encountered a few minor problems when setting it up and couldn&#8217;t resist the temptation to fiddle. Even as i write this the blog theme is not at all how i want but it can wait, i figured i should probably start writing, after all, that is the most important point of the blog non? So why am i actually doing this and who do i think might read it or even care? (I quite like rhetorical questions when writing). I am doing this for several reasons. I am increasingly feel that i want to write things down and share them for some inexplicable reason. We will see how that turns out, i am not holding up much hope. I am very opinionated and love sharing my thoughts on anything that has taken my interest. This is a way of doing so without forcing it upon my dear friends who probably get sick of it (although i [...]]]></description>
				<content:encoded><![CDATA[<p>Well, my first blog post. This has taken me ages to do. I have wanted a blog for quite a while now but never got around to setting it up. It shouldn&#8217;t take ages but i run this on my own web servers and encountered a few minor problems when setting it up and couldn&#8217;t resist the temptation to fiddle. Even as i write this the blog theme is not at all how i want but it can wait, i figured i should probably start writing, after all, that is the most important point of the blog non?</p>
<p>So why am i actually doing this and who do i think might read it or even care? (I quite like rhetorical questions when writing). I am doing this for several reasons. I am increasingly feel that i want to write things down and share them for some inexplicable reason. We will see how that turns out, i am not holding up much hope. I am very opinionated and love sharing my thoughts on anything that has taken my interest. This is a way of doing so without forcing it upon my dear friends who probably get sick of it (although i imagine the only people who will even glance at this are friends and family). I intend to do a lot of writing about subjects linked to my degree in Aeronautical Engineering, this will likely bore anyone that reads it so i admit that it is a device to help me learn. If i am revising a subject, say aerodynamics, and then i write something about it then it will hopefully help with my understanding of it. It might turn out to be the case that the things i write end up being useful to some other poor confused student who stumbles across my blog through a suggestion from Google.</p>
<p>I am interested to see where this goes and would like to think that it will become moderately successful (by which i mean somebody somewhere occasionally glances at it and i am actually motivated and indeed enjoy doing this). For now though i think i will stop as i should probably sleep.</p>
<p>Good Night!</p>
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