Given the digital filter structure of Figure 4.38:

(a) Determine its state-space description.

(b) Compute its transfer function.

(c) Show its transposed circuit.

(d) Use this structure with \(a=-b=\frac{1}{4}\) to design a filter with a unit DC gain to eliminate the frequency \(\omega_{\mathrm{s}} / 2\), where \(\omega_{\mathrm{s}}\) represents the sampling frequency.

Transcribed Image Text:

Fig. 4.38. x(n) -a Digital filter structure for Exercise 4.11. 2 y (n)