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Problems 211
2. From the following values of N, choose the one that will provide the least amount of
leakage in the spectrum of x a(t). Plot the real and imaginary parts of the DFT spectrum
X(k). (a) N = 90, (b) N = 95, (c) N = 99.
P5.39 Using (5.49), determine and draw the signal flow graph for the N =8point, radix-2
decimation-in-frequency FFT algorithm. Using this flow graph, determine the DFT of the
sequence
x(n) =cos (πn/2) , 0 ≤ n ≤ 7
P5.40 Using (5.49), determine and draw the signal flow graph for the N =16point, radix-4
decimation-in-time FFT algorithm. Using this flow graph, determine the DFT of the
sequence
x(n) =cos (πn/2) , 0 ≤ n ≤ 15
P5.41 Let x(n) beauniformly distributed random number between [−1, 1] for 0 ≤ n ≤ 10 6 . Let
h(n) =sin(0.4πn), 0 ≤ n ≤ 100
1. Using the conv function, determine the output sequence y(n) =x(n) ∗ h(n).
2. Consider the overlap-and-save method of block convolution along with the FFT
algorithm to implement high-speed block convolution. Using this approach, determine
y(n) with FFT sizes of 1024, 2048, and 4096.
3. Compare these approaches in terms of the convolution results and their execution times.
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