# Summary13 - Summary 13 Hamid Jafarkhani Digital Signal...

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Summary 13 Hamid Jafarkhani Digital Signal Processing Summary 13 – p. 1/

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Ideal Filters and Causality Ideal filters are not causal. Causality implies H ( ω ) cannot be zero except at a finite set of points in frequency. | H ( ω ) | cannot be constant over a range of frequencies. A transition in | H ( ω ) | cannot be infinitely sharp. Summary 13 – p. 2/
Filter Design by Impulse Invariance Impulse Invariance: A discrete-time system is defined by sampling the impulse response of a continuous-time system h [ n ] = h a ( nT ) H ( ω ) = 1 T summationdisplay k = -∞ H a parenleftbigg j bracketleftbigg ω T + 2 πk T bracketrightbiggparenrightbigg , ω = Ω T Impulse Invariance mapping is z = e sT Summary 13 – p. 3/

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Impulse Invariance
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