Question

A discrete-time signal X(n) is passed through a digital filter h(n) to produce an output signal y(n). The difference equation of the filter is provided below: y(n) = -0.8y(n-1) + 0.2x(n). (a) Provide an expression for the transfer function H(z). (b) Provide the magnitude of the filter in dB at F = 0 Hz and F = 4000 Hz, and give the -3 dB frequency of the filter in Hz if the intended sampling frequency is 8 kHz. (c) Indicate the nature of the filter (bandpass, notch, low pass, high pass).

          A discrete-time signal X(n) is passed through a digital filter h(n) to produce an output signal y(n). The difference equation of the filter is provided below: y(n) = -0.8y(n-1) + 0.2x(n).

(a) Provide an expression for the transfer function H(z).
(b) Provide the magnitude of the filter in dB at F = 0 Hz and F = 4000 Hz, and give the -3 dB frequency of the filter in Hz if the intended sampling frequency is 8 kHz.
(c) Indicate the nature of the filter (bandpass, notch, low pass, high pass).

Added by Christy G.

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