Digital and signal analysis

Investigate and report on the use of Pseudo Binary Random Sequences (PRESS) for determining the underlying dynamics of systems i.e. how are they used for system identification.

i) Obtain the difference equation describing the behaviour of the filter.
ii) Determine the impulse response of the filter.
iii) Find the z-domain transfer function of the system i.e. find Y(z)/X(z).
iv) If the filter was implemented at a sampling frequency of Fs=1oHz, at what frequency would the peak of the magnitude of the frequency response occur ? What magnitude does it have at this frequency?
v) Does it possess a low-pass, high-pass, band-pass or band-stop characteristic
Vi) Check your results with Matlab and include supporting plots and the commands you used.