ECE 513 - DIGITAL SIGNAL PROCESSING
Cranos M. Williams
Assigned: October 2, 2017
HOMEWORK 5 SOLUTION - Due October 9, 2017
1.DFT of Even Part: (15 Pts)The even part of a real sequence x(n) is defined byxe(n) =x(n) +x(-n)2.(1)suppose that x(n) is a real finite-length sequence defined such that x(n) = 0 forn <0andn>N. Let X(k) denote theN-point DFT of x(n).(a) IsRe[X(k)] the DFT ofxe(n)?Why?(b) What is the inverse DFT ofRe[X(k)] in terms ofx(n)?
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ECE 513 - Homework 5
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2.Overlap Add Method: (25 Pts)The length of a sampled speech signal is 63412 samples and the sampling rate is 8000samples per second. We wish to use the overlap–add filtering procedure with a FIRdigital filter with 98 coefficients. We want the block size to be 512 samples. Assumethat the input has been placed in an arrayxand the filter coefficients have been placedin an arraybfor all parts of this problem. Also, assume that you will store the outputin an arrayy.(a) Determine the number of blocks of data that will be used in implementing thefilter. Round any fraction up to the next whole number (assumes that the lastblock will be padded with zeros to make it the appropriate length).(b) Determine the number of zeros that must be added to the filter before computingthe DFT. Give the appropriate Matlab statement to add the required coefficientsand zeros to filter and then compute the required DFT of the filter.(c) Determine the number of zeros that must be added to the first block of data.Determine the number of data values that need to be used in the block of data.Give the appropriate Matlab script to add the required zeros and compute theDFT of the first data block.

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