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system function

H(z), the z-transform of an LTI system's impulse response -- reduces to the frequency response on the unit circle.

The system function H(z) is the z-transform of an LTI system's impulse response h[n], read directly from a difference equation's coefficients. On the unit circle, H(z)|_{z=e^{j\omega}} = H(e^{j\omega}) recovers the ordinary frequency response.

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