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The convolution of [1 2 1] and [1 2 1] will have the highest amplitude at t= _________

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The convolution of [1 2 1] and [1 2 1] will have the highest amplitude at t= _________

(a) 3 units

(b) 0 units

(c) 1 unit

(d) 2 units

I got this question in homework.

Question is taken from Operations on Signals topic in section Digital Signal Processing of MATLAB

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Correct option is (d) 2 units

The best I can explain: If we observe the process of graphical convolution, we find that since, the given two signals are equal to each other, the maximum amplitude of the signal generating due to convolution will be midway between the total length of the resultant signal. This is due to the fact that at that instant, one signal lies on top of another. Now the total length of the convolved signal is 5 units(0,1,2,3,4) and the middle point is t=2. Hence, the correct option is t=2 units.

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