Question

What is the Scope value if the signal generator has a frequency of 2 Hz only?

(a) An attenuated signal of same frequency

(b) The entire signal at the same frequency

(c) The entire signal at reduced frequency

(d) An attenuated signal at reduced frequency

I got this question in examination.

This is a very interesting question from Convolution topic in division Digital Signal Processing of MATLAB

Answer 1

Right answer is (a) An attenuated signal of same frequency

The explanation is: The above transfer function is that of a high pass filter. The cut-off frequency for allowing signals is 3Hz but the given signal frequency is that of 2Hz only. If the frequency of the signal generator was more than 2Hz- the output would’ve been entire signal at the same frequency but for >>3Hz. Now, the convolution in time domain is multiplication in frequency domain and the output of the transfer function block is the product of the transfer function and the laplace transform of the sinusoid. It can be checked in MATLAB that the poles of the resultant function will consist of one pole at s=-2+(-).707i which equivalently suggest that there is a 3 db decade if the input frequency becomes less than 2hz.