28 Jun DIGITAL AND SIGNAL ANALYSIS
PartA “””w
You have been given the impulse response, h[n], ofa digital FIR filter, as shown
in Figurel. You are required to analyse the response of the filter to the particular
input signal x[n], also shown in Figure l.
FIRfiItewith impulse response h[n]
n ylnl
Xlnl – hl l
2 ~ 2
->
0 OUTPUT
0 l 23 …n 1 0 23 …n
INPUT
Figure 1
i) Use convolution to find the output, y[n], of the FIR filter in response to the
specified input, x[n], shown in Figure 1. (10)
ii) Obtain the 2 domain transfer function of the Filter in Figure 1 (note: you
could use your answer to part i) or obtain directly from h[n]). (10)
iii) Use Matlab to plot the frequency response of the 2 transfer function of ii).
Include your plot in your assignment return, and describe how you obtained it.
What type of filter is it ? (LP, HP, BS or BP) (20)
Part B
Figure 2 shows the structure of a digital filter in block diagram form.
i) Obtain the difference equation
describing the behaviour of the filter. + “2)
ii) Determine the impulse response of the X62)
filter. x[“] : y [n
iii) Find the z-domain transfer function of
the system i.e. find Y(z)/X(z).
iv) Ifthe filter was implemented at a _1
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.
Figure 2
Part C (40)
Investi ate and re ort on the u
determining the uiiderlying @3512??? Bmary Random sequences (PRESS) for
YStemS 1-6. hOW are they used for svstem
identification. * (20)
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