Frequency Response from a Discrete Transfer Function

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Homework Statement


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Find the DC Gain and the Frequency Response of the above discrete-time system.

The Attempt at a Solution


This isn't really a homework problem but something I've been struggling with for my exams. I am given a transfer function in terms of z and am asked to find its DC Gain. This is easy enough - I just substitue 1 in place of z and get the DC Gain. I also understand why we put in 1. Its because z = ejw and when w = 0 (i.e DC), z = 1.

However, what I get simply stuck at is how to sketch the frequency response from a given transfer function. I understand that by drawing a pole-zero plot I can get some idea of how the frequency response will look like it but I can never really nail it. For instance, I know that if there are two zeroes on the unit circle the gain is going to fall to 0 at those points.

My problem, in this case, is how do I know what those ponts are in terms of Hz? The zeros are a complex number - how do I translate this complex number to Hz?

Secondly, often in my exams, a quick sketch is asked for the gain and phase of the filter. What's a quick way to sketch this? Am I right in assuming that I just subsitute ejw and use some values for w and then plot the result - would this give me a plot for gain and phase?
 

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