The relationship between the input x[n] and output y[n] of a causal digital filter is given as follows: (a) (b) (c) y[n] = x[n] + x[n − 2] + y[n − 2] Determine the poles and zeros of the system and sketch a plot of them on the z-plane. Determine an expression for the impulse response of the filter using long division. Evaluate the first 5 values of the impulse response. Design a digital filter for the above system using: (i) Direct form-I structure.

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The relationship between the inputx[n]and outputy[n].(

     

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The relationship between the input x[n] and output y[n] of a causal digital filter is
given as follows:
(a)
(b)
(c)
y[n] = x[n] + x[n − 2] + y[n − 2]
Determine the poles and zeros of the system and sketch a plot of them on the
z-plane.
Determine an expression for the impulse response of the filter using long
division. Evaluate the first 5 values of the impulse response.
Design a digital filter for the above system using:
(i)
Direct form-I structure.
(iii)
Minimum number of memory elements.
Analyse the two designs.
Transcribed Image Text:The relationship between the input x[n] and output y[n] of a causal digital filter is given as follows: (a) (b) (c) y[n] = x[n] + x[n − 2] + y[n − 2] Determine the poles and zeros of the system and sketch a plot of them on the z-plane. Determine an expression for the impulse response of the filter using long division. Evaluate the first 5 values of the impulse response. Design a digital filter for the above system using: (i) Direct form-I structure. (iii) Minimum number of memory elements. Analyse the two designs.
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