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Exercises in Digital Signal Processing 1 The Discrete ...

Exercises in Digital Signal ProcessingIvan W. SelesnickJanuary 27, 2015 Contents1 The Discrete Fourier Transform12 The Fast Fourier Transform163 Filters184 Linear-Phase FIR Digital Filters295 Windows386 Least Square Filter Design507 Minimax Filter Design548 Spectral Factorization569 Minimum-Phase Filter Design5810 IIR Filter Design6411 Multirate Systems6812 Quantization7413 Spectral Estimation7514 Speech Filtering8215 More Exercises8616 Old Exercises911 The Discrete Fourier Compute the DFT of the 2-point Signal by hand (without a calculator orcomputer).x= [20,5] Compute the DFT of the 4-point Signal by [3,2,5,1] The even samples of the DFT of a 9-point real signalx(n) are given byX(0) = ,X(2) = + j,X(4) = + j,X(6) = + j,X(8) = j,Determine the missing odd samples of the DFT.

Exercises in Digital Signal Processing Ivan W. Selesnick January 27, 2015 Contents 1 The Discrete Fourier Transform1 2 The Fast Fourier Transform16 3 Filters18 4 Linear-Phase FIR Digital Filters29 5 Windows38 6 Least Square Filter Design50 7 Minimax Filter Design54 8 Spectral Factorization56

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