# Hw3 - method is used(b One can compute the long convolution by using the DFT-based overlap-add algorithm in which the input sequence is segmented

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1. Oppenheim’s book, Chapter 8: 32, 33, 43, 59, 67, 69 2. Oppenheim’s book, Chapter 9: 44, 47 3. A band-limited continuous-time signal ( ) t x a with its spectrum () j X a , as indicated below. Determine the smallest sampling frequency T F , in each case, that is employed to sample ( ) t x a so that it can be fully recovered from its sampled version [] n x . You have to sketch the Fourier transform of the sampled version x [ n ] obtained by sampling ( ) t x a at the sampling rate F T and the frequency response of the ideal reconstruction filter needed to fully recovered () t x a for each case. (a) 2 =200 π , 1 =160 π ; (b) 2 =160 π , 1 =120 π ; (c) 2 =150 π , 1 =110 π ; ( ) j X a 2 1 2 1 4. An input sequence x [n] of length 1024 is to be filtered by a FIR filter h [n] of length 34 . (a) What would be the total number of multiplications if the direct convolution
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Unformatted text preview: method is used? (b) One can compute the long convolution by using the DFT-based, overlap-add algorithm, in which the input sequence is segmented into a set of contiguous blocks of equal length. Each block is then filtered separately, and the overlaps in the output blocks are added appropriately to generate the output convolution. Suppose that the short linear convolutions are performed by Cooley-Tukey (Radix-2) FFT algorithm. Determine the appropriate power-of-2 transform length N , N>34 , that would result in a minimum number of multiplications and calculate the total number of multiplications that would be required....
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## This note was uploaded on 08/23/2009 for the course IEE 5036 taught by Professor Cwliu during the Fall '05 term at National Chiao Tung University.

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