Find the impulse response and frequency response of a discrete time system described by the difference equation $$ \mathbf{y}(\mathbf{n})-\mathbf{y}(\mathbf{n}-\mathbf{1})+\frac{3}{16} \mathbf{y ( n - 2 )}=\boldsymbol{x ( n )}+\frac{1}{3} x(\mathbf{n}-\mathbf{1}) $$

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Huff Bright · Accepted Answer

The impulse response $$h(n)$$ is found by taking the inverse Z-transform of the transfer function $$H(z)$$, and the frequency response $$H(e^{j\omega})$$ is obtained by substituting $$z = e^{j\omega}$$ into $$H(z)$$.

Find the impulse response and frequency response of a discrete time system described by the difference equation \( \mathbf{y}(\mathbf{n})-\mathbf{y}(\mathbf{n}-\mathbf{1})+\frac{3}{16} \mathbf{y ( n - 2 )}=\boldsymbol{x ( n )}+\frac{1}{3} x(\mathbf{n}-\mathbf{1}) \)

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Find the impulse response and frequency response of a discrete time system described by the difference equation \( \mathbf{y}(\mathbf{n})-\mathbf{y}(\mathbf{n}-\mathbf{1})+\frac{3}{16} \mathbf{y ( n - 2 )}=\boldsymbol{x ( n )}+\frac{1}{3} x(\mathbf{n}-\mathbf{1}) \)

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