Question

An LTI system S is cascaded in series with two other non-LTI systems as follows: x(t) w(t) S S: LTI z(t) S2 y(t) H(j?) The system S? is given by: And the system S? is: w(t) = x(t/2) y(t) = z(2t) The system S has H(j?) as its frequency response. (This question continues on the next page.) (a) Find how Y(j?) is related to X(j?), in terms of H(j?). Deduce the overall frequency response $H_{eq}(j?) = \frac{Y(j?)}{X(j?)}$. (b) If H(j?) is given by: $H(j?) = \frac{2a - j?}{2a + j?}$ where a > 0, find the impulse response h(t) of the system S. Deduce the overall impulse response $h_{eq}(t)$.

          An LTI system S is cascaded in series with two other non-LTI systems as follows:
x(t) w(t) S S: LTI z(t) S2 y(t)
H(j?)
The system S? is given by:
And the system S? is:
w(t) = x(t/2)
y(t) = z(2t)
The system S has H(j?) as its frequency response.
(This question continues on the next page.)
(a) Find how Y(j?) is related to X(j?), in terms of H(j?). Deduce the overall
frequency response $H_{eq}(j?) = \frac{Y(j?)}{X(j?)}$.
(b) If H(j?) is given by:
$H(j?) = \frac{2a - j?}{2a + j?}$
where a > 0, find the impulse response h(t) of the system S. Deduce the overall impulse
response $h_{eq}(t)$.

An LTI system S is cascaded in series with two other non-LTI systems as follows:
x(t) w(t) S S: LTI z(t) S2 y(t)
H(j?)
The system S? is given by:
And the system S? is:
w(t) = x(t/2)
y(t) = z(2t)
The system S has H(j?) as its frequency response.
(This question continues on the next page.)
(a) Find how Y(j?) is related to X(j?), in terms of H(j?). Deduce the overall
frequency response Heq(j?) = (Y(j?))/(X(j?)).
(b) If H(j?) is given by:
H(j?) = (2a - j?)/(2a + j?)
where a > 0, find the impulse response h(t) of the system S. Deduce the overall impulse
response heq(t).

Added by Agust-N R.

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