Question

Consider an IIR filter with impulse response $h[n] = (\frac{1}{3})^n u[n]$. The input signal $x[n] = 3^n u[-n - 1]$ is entered into the IIR filter to generate the output signal $y[n]$. (a) (11%) Determine the transfer function $H(z)$ of the IIR filter. Remember to state the ROC of $H(z)$. Draw the pole-zero plot of $H(z)$, and explain whether the IIR filter is stable or not. (b) (6%) Determine the z-transform $X(z)$ of the input signal $x[n]$. Remember to state the ROC of $X(z)$. (c) (15%) Determine the output signal $y[n]$, i.e., give an expression for $y[n]$. Useful z-transform results: $\cdot a^n u[n] \leftrightarrow \frac{z}{1 - az^{-1}}$, ROC = $\{|z| > |a|\}$ $\cdot -a^n u[-n - 1] \leftrightarrow \frac{z}{1 - az^{-1}}$, ROC = $\{|z| < |a|\}$

Name: consider an iir filter with impulse response hn frac13n un the input signal xn 3n u n 1 is entered into the iir filter to generate the output signal yn a 11 determine the transfer function h 12377
Uploaded: 2024-05-09T06:03:52-08:00
Duration: 1 min 8 s
Channel: Adi S
Description: consider an iir filter with impulse response hn frac13n un the input signal xn 3n u n 1 is entered into the iir filter to generate the output signal yn a 11 determine the transfer function h 12377

          Consider an IIR filter with impulse response $h[n] = (\frac{1}{3})^n u[n]$. The input signal $x[n] = 3^n u[-n - 1]$ is entered into the IIR filter to generate the output signal $y[n]$.
(a) (11%) Determine the transfer function $H(z)$ of the IIR filter. Remember to state the ROC of $H(z)$. Draw the pole-zero plot of $H(z)$, and explain whether the IIR filter is stable or not.
(b) (6%) Determine the z-transform $X(z)$ of the input signal $x[n]$. Remember to state the ROC of $X(z)$.
(c) (15%) Determine the output signal $y[n]$, i.e., give an expression for $y[n]$.
Useful z-transform results:
$\cdot a^n u[n] \leftrightarrow \frac{z}{1 - az^{-1}}$, ROC = $\{|z| > |a|\}$
$\cdot -a^n u[-n - 1] \leftrightarrow \frac{z}{1 - az^{-1}}$, ROC = $\{|z| < |a|\}$

$consider an iir filter with impulse response hn frac13n un the input signal xn 3n u n 1 is entered into the iir filter to generate the output signal yn a 11 determine the transfer function h 12377$

Added by Manuel P.

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