Consider the following IIR filter.

The initial input data sequence is given by x_n = [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.

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.