A question regarding z transform and its magnitude response

1. How do you find the magnitude of a frequency response?
2. What is the use of the magnitude response of system response?
3. What is the physical significance of Z-transform?

How do you find the magnitude of a frequency response?

First we substitute s = jω into H(s) to obtain an expression of the frequency response. Note that the numerator and the denomator are both complex. To obtain the amplitude response, we take the absolute value of H(jω). To do this, we evaluate the magnitude of the numerator and the denominator separately.

What is the use of the magnitude response of system response?

In most cases, the magnitude response is the ratio of the amplitude of frequencies in the output signal to the amplitude of frequencies of the input signal. Usually, if we want to describe how a system impacts the amplitudes of frequencies in a signal, we will use the term magnitude response.

What is the physical significance of Z-transform?

z transforms are particularly useful to analyze the signal discretized in time. Hence, we are given a sequence of numbers in the time domain. z transform takes these sequences to the frequency domain (or the z domain), where we can check for their stability, frequency response, etc.