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(ej") is actually real-valued. What is the output of the filter when the input is x[n] = cos(@n) (for all n n)? For what %3D value(s) of w is the output zero for all n?

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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]
1)
Show that the complex frequency response H(ej") 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?
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] 1) Show that the complex frequency response H(ej") 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?
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