Consider the second-order differencing filter described by the input-output relationship y[n] = x[n+ 1] – 2x[n] + x[n – 1] %3D 1) Show that the complex frequency response H(el®) is actually real-valued. What is the output of the filter when the input is x[n] = cos(wn) (for all n n)? For what value(s) of w is the output zero for all n? II) Determine and sketch the response y[·] of the filter to the input signal n > 0 n = 0 3-n x[n] = -3n

Introductory Circuit Analysis (13th Edition)
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Consider the second-order differencing filter described by the input-output relationship
y[n] = x[n + 1] – 2x[n] + x[n – 1]
I)
Show that the complex frequency response H(ela) is actually real-valued.
What is the output of the filter when the input is x[n] = cos(wn) (for all n n)? For what
%3D
value(s) of w is the output zero for all n?
II)
Determine and sketch the response y[:] of the filter to the input signal
3-n
n > 0
x[n]
|
0 = u
-3n
n < 0
Transcribed Image Text:Consider the second-order differencing filter described by the input-output relationship y[n] = x[n + 1] – 2x[n] + x[n – 1] I) Show that the complex frequency response H(ela) is actually real-valued. What is the output of the filter when the input is x[n] = cos(wn) (for all n n)? For what %3D value(s) of w is the output zero for all n? II) Determine and sketch the response y[:] of the filter to the input signal 3-n n > 0 x[n] | 0 = u -3n n < 0
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