Assignment:
The below system acts as an analog filter. The analog signal m(t) is passed through an analog to digital converter and m(k) is the resultant discrete or digital output in the form e(jw). The discrete signal m(k) in the form e(jw) is applied to the discrete filter h(k) with an impulse response of h (k) = (0.5) k u (k). This is in essence the transfer function of a LTI system. The transfer function is described below:
m(k) = ejwk→
→x(k) = h(ejw) * ejwk
The resultant discrete signal x(k) in the form of ejwk is then fed into a digital to analog converter with the output being an analog signal p(t). In summary the filter takes an analog signal m(t), converts it to discrete sequence m(k),filters the signal x(k) and converts the signal back to analog p(t)
The sampling rate in the A/D and D/A is 100 samples/second, and the impulse response in the figure above is h (k) = (0.5) k u (k).
(a) What is the digital frequency m (k) in the form e(jw) if ma (t) = 3cos(20πt)
dfdfdsa
(b) Find the steady-state analog signal pa (t) at the output if ma (t) = 3cos(20πt)
dfdfdsa
(c) Find the steady-state analog signal pa (t) at the output if ma (t) = 3u (t)
dfdfdsa
(d) Find two other analog signals ma (t), with different analog frequencies, that will produce the same steady state output pa (t) when ma (t) = 3cos(20πt) is applied.
dfdfdsa
(e) To prevent aliasing, a prefilter would be required to process ma (t) before it passes to the A/D converter. What type of filter should be used, and what should be its largest cutoff frequency for the given configuration to work well?
dfdfdsa