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hw7_600(2) - ECE-600 Homework#7 Introduction to Digital...

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ECE-600 Introduction to Digital Signal Processing Autumn 2010 Homework #7 Nov. 12, 2010 HOMEWORK ASSIGNMENT #7 Due Fri. Nov. 19, 2010 (in class) 1. Consider the N -DFT sequence { X [ k ] } N - 1 k =0 and the frequency-reversed version Y [ k ] = X [ N 1 k ] for k = 0 , 1 ,...,N 1. Note that this type of frequency-reversal is different from the version X [ (− k ) N ] that we saw in lecture. In Matlab, this new type of reversal can be implemented by the command fliplr . (a) Find an expression for { y [ n ] } N - 1 n =0 , the IDFT of { Y [ k ] } , in terms of { x [ n ] } N - 1 n =0 , the IDFT of { X [ k ] } . (b) Test your answer in Matlab for the case N = 8 using the randomly generated signal X=randn(1,8) , by evaluating max(abs( ifft(fliplr(X),N) - ***)) , where *** is your derived expression involving the DFT samples x=ifft(X,N) . 2. Say that you have two real-valued length- N DFT sequences { A [ k ] } and { B [ k ] } whose IDFTs you want to compute. While you could take two separate N -IDFTs, there is a more clever approach that saves complexity by using only one N -IDFT. The key is to realize that the standard IDFT is
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