Chapter 3: Fourier Representation of Signals and LTI Systems
Properties of LTI systems
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Properties of LTI systems • Commutative: x[n]¤h[n] = h[n]¤x[n] • Distributive: x[n]¤(h 1 [n] + h 2 [n]) = x[n]¤h 1 [n] + x[n] ¤h 2 [n] • Associative: x[n]¤(h 1 [n]¤h 2 [n]) = (x[n]¤h 1 [n])¤h 2 [n] h 1 [n] h 2 [n] h 1 [n] ¤ h 2 [n] x[n] x[n] y[n] y[n] h[n] x[n] y[n] x[n] h[n] y[n] h 1 [n] h 2 [n] x[n] + y[n] h 1 [n] + h 2 [n] x[n] y[n]
description
Properties of LTI systems. Commutative: x[n] ¤ h[n] = h[n] ¤ x[n] Distributive: x[n] ¤ (h 1 [n] + h 2 [n]) = x[n] ¤ h 1 [n] + x[n] ¤ h 2 [n] Associative: x[n] ¤ (h 1 [n] ¤ h 2 [n]) = (x[n] ¤ h 1 [n]) ¤ h 2 [n]. x[n]. h[n]. y[n]. h[n]. x[n]. y[n]. h 1 [n]. y[n]. x[n]. x[n]. - PowerPoint PPT Presentation
Transcript of Properties of LTI systems
Properties of LTI systems
• Commutative: x[n]¤h[n] = h[n]¤x[n]
• Distributive: x[n]¤(h1[n] + h2[n]) = x[n]¤h1[n] + x[n]¤h2[n]
• Associative: x[n]¤(h1[n]¤h2[n]) = (x[n]¤h1[n])¤h2[n]
h1[n] h2[n]
h1[n] ¤ h2[n]
x[n]
x[n]
y[n]
y[n]
h[n]x[n] y[n] x[n]h[n] y[n]
h1[n]
h2[n]
x[n]+ y[n] h1[n] + h2[n]x[n] y[n]
