Construct the corresponding transfer function, Electrical Engineering

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Consider the following IIR filter.

The initial input data sequence is given by xn = [10 15 20 15 8 6 9 0 0 0]
Construct a table that shows the corresponding signal values at A and B and hence the output sequence. Assume that the initial values at A & B are zero.

Construct the corresponding transfer function H(z) for this filter.

1727_Construct the corresponding transfer function.png

Use MATLAB to confirm the system output as recorded in your table.

Construct the corresponding impulse function for this filter by finding Z-1 {H(z)}. Use MATLAB  to obtain the same impulse response & produce an equivalent stem plot. (Can you check out even  more using MAPLE ?)

Find the corresponding singularities (poles & zeros) of this Transfer Function & position them on a map of the complex plane. Use this map to illustrate the frequency response of the filter at Π/4 ; Π/3 and calculate the magnitude & phase response at these two frequencies. Find the full graphical frequency response (magnitude & phase) of this filter. (The MATLAB function fvtool will be useful at this stage.). Do the two points calculated above position themselves correctly on this graph.


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