Question

We want to perform the convolution of x(n) and h(n). Assume x(n) is zero outside 0 ? n < 300. Assume h(n) is zero outside 0 ? n < 50. Assume x(n) and h(n) are complex- valued in general. Determine the approximate number of complex multiplications required to compute the convolution sum directly. Next, determine the approximate number of complex multiplications required to convolve the signals using the radix-2 Cooley-Tukey FFT algorithm, where the FFT size must be a power of 2. (We must compute two forward FFTs, then multiply X(k) and H(k), and then do an inverse FFT.) Assuming that complex multiplications are the most significant portion of the required computation, what is the approximate speed-up factor (rounded to integer) when we use FFTs instead of the convolution sum? 5 2 4 None of the other answers is correct 3

          We want to perform the convolution of x(n) and h(n). Assume x(n) is zero outside 0 ?
n < 300. Assume h(n) is zero outside 0 ? n < 50. Assume x(n) and h(n) are complex-
valued in general. Determine the approximate number of complex multiplications
required to compute the convolution sum directly. Next, determine the approximate
number of complex multiplications required to convolve the signals using the radix-2
Cooley-Tukey FFT algorithm, where the FFT size must be a power of 2. (We must
compute two forward FFTs, then multiply X(k) and H(k), and then do an inverse FFT.)
Assuming that complex multiplications are the most significant portion of the
required computation, what is the approximate speed-up factor (rounded to integer)
when we use FFTs instead of the convolution sum?
5
2
4
None of the other answers is correct
3

We want to perform the convolution of x(n) and h(n). Assume x(n) is zero outside 0 ?
n < 300. Assume h(n) is zero outside 0 ? n < 50. Assume x(n) and h(n) are complex-
valued in general. Determine the approximate number of complex multiplications
required to compute the convolution sum directly. Next, determine the approximate
number of complex multiplications required to convolve the signals using the radix-2
Cooley-Tukey FFT algorithm, where the FFT size must be a power of 2. (We must
compute two forward FFTs, then multiply X(k) and H(k), and then do an inverse FFT.)
Assuming that complex multiplications are the most significant portion of the
required computation, what is the approximate speed-up factor (rounded to integer)
when we use FFTs instead of the convolution sum?
5
2
4
None of the other answers is correct
3

Added by James V.

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