1. Convolution in the time domain is equivalent to what mathematical operation i

Question

1.       Convolution in the time domain is equivalent to what mathematical operation in the frequency domain?

2.       When we convolve the triangular 10 Hz input with the impulse response of the 50 Hz low-pass filter, why is it that the peaks of output become rounded and not a sharp point as in the input triangular function?

3.       Why is it that we get no (or very little) output when we convolve the 60 Hz sinusoid with the impulse response of the filter?

4.       When we apply the 10 Hz output, which is within the pass band of the filter, we see that we get nearly the same sinusoid in the output except for a time delay. How is the time delay a signal experiences as it passes through a system related to the phase characteristic of the system response?

Explanation / Answer

1Ans)

Convolution in the time domain is represented in the frequency domain by a multiplying the amplitude spectra and adding the phase spectra.

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