Question

Consider the system in the figure below where w[n] = (-1)$^n$x[n], y[n] = (-1)$^n$z[n], H(?) is the frequency response of the system with input w[n] and output z[n]. Let G(?) be the frequency response of the overall system (input x[n] and output y[n]). (a) Evaluate the DTFT of w[n]: W(?) = (b) Evaluate the DTFT of z[n]: Z(?) = (c) Evaluate the DTFT of y[n]: Y(?) = (d) Using the result of part (c) above evaluate G(?) = (e) Assume that H(?) is an ideal lowpass filter with cutoff frequency ?/3 (i.e the passband is |?| ? ?/3). Plot its frequency response. (f) Plot the frequency response G(?) corresponding to H(?) in part (e). What type of filter is this?

          Consider the system in the figure below where w[n] = (-1)$^n$x[n], y[n] = (-1)$^n$z[n],
H(?) is the frequency response of the system with input w[n] and output z[n]. Let
G(?) be the frequency response of the overall system (input x[n] and output y[n]).
(a) Evaluate the DTFT of w[n]: W(?) =
(b) Evaluate the DTFT of z[n]: Z(?) =
(c) Evaluate the DTFT of y[n]: Y(?) =
(d) Using the result of part (c) above evaluate G(?) =
(e) Assume that H(?) is an ideal lowpass filter with cutoff frequency ?/3 (i.e
the passband is |?| ? ?/3). Plot its frequency response.
(f) Plot the frequency response G(?) corresponding to H(?) in part (e). What
type of filter is this?

Consider the system in the figure below where w[n] = (-1)^nx[n], y[n] = (-1)^nz[n],
H(?) is the frequency response of the system with input w[n] and output z[n]. Let
G(?) be the frequency response of the overall system (input x[n] and output y[n]).
(a) Evaluate the DTFT of w[n]: W(?) =
(b) Evaluate the DTFT of z[n]: Z(?) =
(c) Evaluate the DTFT of y[n]: Y(?) =
(d) Using the result of part (c) above evaluate G(?) =
(e) Assume that H(?) is an ideal lowpass filter with cutoff frequency ?/3 (i.e
the passband is |?| ? ?/3). Plot its frequency response.
(f) Plot the frequency response G(?) corresponding to H(?) in part (e). What
type of filter is this?

Added by Benjamin H.

Question

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