DSPY2004Final - DSP Final Examination PART-I. Conceptual...

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DSP Final Examination PART-I. Conceptual Problems: (50%) (Close Book) 1-1. Explain the following four terminologies: (20%) (a) Decimation in Frequency FFT (8-point); (b) Row-Column 2D FFT Method; (c) General Discrete Transform; (d) FIR Filter Design by Windowing. 1-2. There are eight FIR filters, whose impulse responses (starting from n = 0) are h 1 ( n ) : [3, 1, 2, 1, 3]; h 2 ( n ) : [3, 1, 2, 2, 1]; h 3 ( n ) : [3, 1, 2, 1, 2]; h 4 ( n ) : [4, 2, -1, -1, 2, 4]; h 5 ( n ) : [4, 2, -3, 3, -2, -4]; h 6 ( n ) : [4, 2, -3, 5, -3, 2]; h 7 ( n ) : [4, 2, -3, -5, 3, -2]; h 8 ( n ) : [1, 3, 2, -4, 6, 2]. Please give your decision reasons first and identify which filters are (a) Linear phase filter (7%) (b) H i [ k ] (the DFT of h i [ n ]) is real for all k (8%) 1-3. Explain the following three convolutions (10%) (a) Linear Convolution; (b) Periodic Convolution; (c) Circular Convolution; For what condition (what kind of data), these three convolutions will be the same. (5%) PART II. DFT Properties and Computation (60%) 2-1. An 8-point sequence is given as x 8 [ n ] = [3 4 -2 7 -4 1 -5 2], its DFT is expressed by X 8 [ k ]. By 16-point DFT program, we can compute X 16 [ k ] = DFT 16 ( x [ n ]), where we pad 8 extra zeros in the end). Please
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DSPY2004Final - DSP Final Examination PART-I. Conceptual...

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