Consider the following LTI system S, that is characterized by its input -output relationship, where x[n] and y[n] is the input and output signals, respectively. S: yln] = n)-x[n-1] a) Calculate the frequency response H(1) for the system S and plot the amplitude of H(M) for the range of N between 0 and 2n. b) Is the system S a low-pass filter, high-pass filter, or band-pass filter? State your reasoning clearly.

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Consider the following LTI system S, that is characterized by its input -output relationship, where x[n]
and y[n] is the input and output signals, respectively.
S: y[n] = ln]=x[n-1]
a) Calculate the frequency response H(N) for the system S and plot the amplitude of H(N) for the
range of N between 0 and 27.
b) Is the system S a low-pass filter, high-pass filter, or band-pass filter? State your reasoning
clearly.
Transcribed Image Text:Consider the following LTI system S, that is characterized by its input -output relationship, where x[n] and y[n] is the input and output signals, respectively. S: y[n] = ln]=x[n-1] a) Calculate the frequency response H(N) for the system S and plot the amplitude of H(N) for the range of N between 0 and 27. b) Is the system S a low-pass filter, high-pass filter, or band-pass filter? State your reasoning clearly.
Expert Solution
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Linear time invariant (LTI) systems are characterized by its input-output relation ship called difference equations. It can also be characterized by its impulse response.

If the system output does not depends on past outputs it is called FIR (finite impulse response) filters. IIR (infinite impulse response filters) depends on the past outputs also.  Impulse response of FIR filters are finite duration and impulse response of IIR filters are infinite duration.

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