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Minor2 paper dsp , IIT DELHI ,2012

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EEL319 Digital Signal Processing Minor II, 2012-2013, Semester I Name Entry no. Grp no. 1) (10 marks) In the gure below, write down the expression for Y [k ] asuming x[n] is a sequence of length N . First assume Z that L = 0 so that W [k ] = Y [k ]. For this case, express w[n] in terms of x[n]. Then repeat for the case when L = 1. Note that the 1st and 4th blocks from the left are interpolaters by a factor of two, and insert one zero after every input sample. 2) (6 marks) Let x[n] = sin( nK/N ) sin( n/N ) 2 for some interger K . What is the DFT X [k ] of this sequence? For K = 3N/4, assuming N is a multiple of 4, sketch the DFT X [k ]. 3) (6 marks) Consider a system with zeros at 0.5j , 2j , 0.5j , and 2j . Plot the magnitude and phase response in the space below using geometric considerations, clearly indicating the calculations at any one frequency. It may be helpful to write down the frequency response. 4) (6 marks) Let x[n] be an N length sequence. Let M Q = N where M and Q are integers. Let y [n] = Q 1 i=0 x[(n iM )N ] be an N length sequence derived from it. Express Y [k ] in terms of X [k ]. 5) (7 marks) Sketch carefully on the next page a 9-point radix-3 FFT, starting with every third sample of the input sequence.

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