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    Sampling rate, Systems function, Region of convergence

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    ** Please see the attached file for the complete problem description **

    1. If the -3dB cut-off point for the filter shown (in the attachment) occurs for a real frequency of 200Hz then what should be the sampling rate (samples per sec)?

    2. The difference equation for a digital filter is given by: y(n) = 2y(n-1) + y(n-2) + x(n) - x(n-1). Compute the systems function H(z).

    3. Why must the Region of Convergence (ROC) be included with an analytic expression of the z-transform?

    4. True or False and Why: The FIR filter realization has fewer coefficients than an IIR filter but the FIR filter has stability problems that the IIR filter does not.

    5. For a causal LTI system what can you say about the poles of the z transform and the boundary of the region of convergence.

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    Solution Preview

    ** Please see the attached document for the complete solution response **

    On the x-axis, the normalized frequency of pi is equivalent to the frequency fs/2, where fs is the sampling frequency. The -3dB cut-off point is at 0.2*pi which is corresponding to 200Hz. Then the normalized frequency of pi is corresponding to 200/0.2 which is 1000Hz= fs/2. ...

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