Understanding The Fourier Transform
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Understanding The Fourier Transform
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Re: Understanding The Fourier Transform
#2You might be interested in the discussion from one of the previous submissions of this:
http://news.ycombinator.com/item?id=2555562
Here are some other items about the Fourier transform:
Re: Understanding The Fourier Transform
#3You can also think of the Fourier Transform as a projection (dot product) of a signal onto the space of all sinusoids. That's the explanation that made everything click for me.
Re: Understanding The Fourier Transform
#4I would like to see more of these articles cover the phase portion.
Re: Understanding The Fourier Transform
#5I really liked where he color coded the equation and the sentence describing how it worked. I've seen tables in the past explaining what each variable represented, but this was much clearer.
http://altdevblogaday.com/wp-content/uploads/2011/05/Derived...
Re: Understanding The Fourier Transform
#6You can also think of the Fourier Transform as a projection (dot product) of a signal onto the space of all sinusoids. That's the explanation that made everything click for me.
That's a really great way of thinking about it, actually - particularly if you're used to vector mathematics.
Re: Understanding The Fourier Transform
#7This is an interesting way to visualize it, but I think the only way to really grok the Fourier transform is to use it in several different applications, and understand its role in each.
A particularly helpful tangent is to play with convolution and see the many different applications that is useful for (did you know that the shadow cast by an object is its cross section convolved with the cross section of the light source?). Once you really get convolution, and really get its relationship to the Fourier transform, you will be well along the path to enlightenment.
Re: Understanding The Fourier Transform
#8I really liked where he color coded the equation and the sentence describing how it worked. I've seen tables in the past explaining what each variable represented, but this was much clearer. http://altdevblogaday.com/wp-content/uploads/2011/05/Derived...
I nearly got the light blue and green confused, and I have normal color vision. I think there are reasons to prefer tables, or perhaps something animated or interactive would work as well. (e.g. mouseover a term to get its description.)
Re: Understanding The Fourier Transform
#9I really liked where he color coded the equation and the sentence describing how it worked. I've seen tables in the past explaining what each variable represented, but this was much clearer. http://altdevblogaday.com/wp-content/uploads/2011/05/Derived...
I nearly got the light blue and green confused, and I have normal color vision. I think there are reasons to prefer tables, or perhaps something animated or interactive would work as well. (e.g. mouseover a term to get its description.)
>I nearly got the light blue and green confused, and I have normal color vision. //
Define normal.
I have some difficulty differentiating blues and greens sometimes but I found those shades to be quite distinct even on a low quality screen.
Perhaps your colour differentiation is worse than you think? It could be down to monitor settings though, for example.
There's an Ishihara test here - http://colorvisiontesting.com/ishihara.htm FWIW but I'd imagine you'd need to see an optician to do it correctly.
Re: Understanding The Fourier Transform
#10When I first came across Fourier transforms I just thought of it as a bunch of sine and cosine waves destructively/constructively interfering. Could be because we derived FT in class starting by matching sine/cosines to intersect various points.