SYDE252 Lecture Notes - Fourier Series, Kolmogorov Space, Dirac Delta Function
22 Nov 2012
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Document Summary
The forward and inverse fourier transform are defined for aperiodic signal as: Fourier series is used for periodic signals. It"s really not so hard you can do it with your pencil, You"ve got a brand new function the fourier transformation! What a prism does to sunlight, what the ear does to sound, Fourier does to signals, it"s the coolest trick around. Now ltering is easy, you don"t need to convolve; All you do is multiply in order to solve. Think of a delay, a simple shift in time. It becomes a phase rotation now that"s truly sublime! Divide instead of multiply you can do it too. It"s mapped to a delta, in frequency not time. Now take that same delta as a function of time. Sine x on x is handy, let"s call it a sinc. Its fourier transform is simpler than you think. You get a pulse that"s shaped just like a top hat.
