The figure below shows a system commonly used to obtain a highpass filter from a lowpass filter and vice versa. x(t) H() y(t) (a) Show that, if H(jw) is a lowpass filter with cutoff frequency wip, the overall system corresponds to an ideal highpass filter. Determine the system's cutoff frequency and sketch its impulse response (b) Show that, if H(jw) is an ideal highpass filter with cutoff frequency whp the overall system corre- sponds to an ideal lowpass filter, and determine the cutoff frequency of the system.

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The figure below shows a system commonly used to obtain a highpass filter from a lowpass filter and vice
versa.
x(t)
Ho
y(t)
(a) Show that, if H (jw) is a lowpass filter with cutoff frequency wip, the overall system corresponds to
an ideal highpass filter. Determine the system's cutoff frequency and sketch its impulse response
(b) Show that, if H (jw) is an ideal highpass filter with cutoff frequency whp the overall system corre-
sponds to an ideal lowpass filter, and determine the cutoff frequency of the system.
Transcribed Image Text:The figure below shows a system commonly used to obtain a highpass filter from a lowpass filter and vice versa. x(t) Ho y(t) (a) Show that, if H (jw) is a lowpass filter with cutoff frequency wip, the overall system corresponds to an ideal highpass filter. Determine the system's cutoff frequency and sketch its impulse response (b) Show that, if H (jw) is an ideal highpass filter with cutoff frequency whp the overall system corre- sponds to an ideal lowpass filter, and determine the cutoff frequency of the system.
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