dorf_hst15_keyer - Com sys 1 lecture 2 Fourier analyses...

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Com sys 1 lecture 2 Fourier analyses Erik Steuten & Cees keyer
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Chapter 15 Dorf Time versus frequency, How to analyse time signals How to convert signals in time to signals in frequency. Special functions. Fourier transform MATH :(
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The Fourier series. A Fourier series is an accurate representation of a periodic signal and consists of the sum of sinusoids at the fundamental and harmonic frequencies. Definition: A periodic function f t = f t nT n ∈ℤ Example: f t = sin  t 2n 
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A Fourier series General definition: f t = n =−∞ e jn 0 t And obviously (from “signalen 1”) e jn 0 t = cos n 0 t  j sin n 0 t So every function in time could be represented as an infinite sum of sine and cosine waves.
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f t = n =−∞ e jn 0 t After some manipulation and ignoring negative and imaginary time/frequencies f t = a 0 n = 1 a n cos n 0 t  n = 1 b n sin n 0 t f t = c 0 n = 1 c n cos n 0 t  n Only idiots will go for infinity f t = c 0 n
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This note was uploaded on 03/19/2010 for the course E-TECH e-tech taught by Professor Keijer during the Spring '10 term at Hogeschool Utrecht.

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dorf_hst15_keyer - Com sys 1 lecture 2 Fourier analyses...

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