In Matlab circular convolution may be computed efficiently b

In Matlab, circular convolution may be computed efficiently by ifft (fft(x, n). * fft (h, N)). Suppose this method is used to perform linear convolution of the signal x[n], n = 0, 1,, 79999 with the filter impulse response h[n], n = 0, 1,, 80. What value of n should be used to cause circular convolution to compute linear convolution. (this is a zero padding question.)

Solution

x(n) has 80000 samples and h(n) has 81 samples.The linear convolution of x(n) and h(n) has got 80000+81-1=80080 samples.

To perform circular convolution both the signals must have same number of samples and the result is also same number of samples.

so N=80080