kb:bibo_stability

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kb:bibo_stability [2021-05-05 01:02] – ↷ Page moved from kb:ee:bibo_stability to kb:bibo_stability jaeyoungkb:bibo_stability [2024-04-30 04:03] (current) – external edit 127.0.0.1
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 $$ \sum_{n=-\infty}^{\infty} |h[n]| < \infty $$ $$ \sum_{n=-\infty}^{\infty} |h[n]| < \infty $$
  
-A BIBO stable system is guaranteed to have a [[kb:ee:fourier_transform]], since:+A BIBO stable system is guaranteed to have a [[kb:fourier_transform]], since:
  
 $$ |H(j\omega)| = |\int_{-\infty}^{\infty} h(t) e^{-j\omega t} dt| \leq \int_{-\infty}^{\infty} |h(t)| dt < \infty $$ $$ |H(j\omega)| = |\int_{-\infty}^{\infty} h(t) e^{-j\omega t} dt| \leq \int_{-\infty}^{\infty} |h(t)| dt < \infty $$
  
-We can use this property to conclude that the [[kb:ee:region_of_convergence|region of convergence]] of any BIBO stable system must include the Fourier transform. In the [[kb:ee:z-transform|z-domain]], the Fourier transform corresponds to a unit circle in the complex z-plane, and in the [[kb:ee:laplace_transform|Laplace domain]], the Fourier transform corresponds to the imaginary axis.+We can use this property to conclude that the [[kb:region_of_convergence|region of convergence]] of any BIBO stable system must include the Fourier transform. In the [[kb:z-transform|z-domain]], the Fourier transform corresponds to a unit circle in the complex z-plane, and in the [[kb:laplace_transform|Laplace domain]], the Fourier transform corresponds to the imaginary axis.
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