What is the system function of the equivalent digital filter? H(z) = Y(z)/X(z) = ?(a) \(\frac{(\frac{bT}{2})(1+z^{-1})}{1+\frac{aT}{2}-(1-\frac{aT}{2}) z^{-1}}\)(b) \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\)(c) \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+a)}\)(d) \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\) & \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+a)}\)This question was addressed to me in an interview for job.I want to ask this question from IIR Filter Design by the Bilinear Transformation in chapter Discrete Time Systems Implementation of Digital Signal Processing

What is the system function of the equivalent digital filter? H(z) = Y

1.	What is the system function of the equivalent digital filter? H(z) = Y(z)/X(z) = ?(a) \(\frac{(\frac{bT}{2})(1+z^{-1})}{1+\frac{aT}{2}-(1-\frac{aT}{2}) z^{-1}}\)(b) \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\)(c) \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+a)}\)(d) \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\) & \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+a)}\)This question was addressed to me in an interview for job.I want to ask this question from IIR Filter Design by the Bilinear Transformation in chapter Discrete Time Systems Implementation of Digital Signal Processing
Answer» The CORRECT choice is (d) \(\frac{(\frac{BT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\) & \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+a)}\) Explanation: As we considered analog linear filter with system FUNCTION H(s) = b/s+a Hence, we got an equivalent system function where, s = \(\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}})\).

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