Fourier Series ON THE COLLEGE OF ARTS OF SCIENCE.pptx

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1. Fourier Series in signal processing

2. INTROduction What is Fourier Series?

3. Developed by joseph Fourier A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions f(x)=a0/2+ ∑ ∞ ( ancosn π x/L + bnsinn π x/L) n =1

4. Formulae:

5. application Signal processing

6. Signal processing First and foremost, a Fourier series of a signal tells you  what frequencies are present in your signal and in what proportions .

7. Signal processing The magnitude square of the Fourier series solution , instantly tells us how much power the signal  x ( t ) has at a particular frequency  f . ∫ r | x ( t )|^2  dt = ∫ r | X ( f )|^2  df

8. Signal processing By being able to split signals into their constituent frequencies, one can easily block out certain frequencies selectively by nullifying their contributions.