12.2: Transformadas Z comunes
- Page ID
- 86416
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| Señal | Transformación Z | Región de Convergencia |
|---|---|---|
| \(\delta(t)\) | \(1\) | todos\(s\) |
| \(\delta(t-T)\) | \(e^{-(sT)}\) | todos\(s\) |
| \(u(t)\) | \(\frac{1}{s}\) | \(\mathbb{R}>0\) |
| \(−u(−t)\) | \(\frac{1}{s}\) | \(\mathbb{R}<0\) |
| \(tu(t)\) | \(\frac{1}{s^2}\) | \(\mathbb{R}>0\) |
| \(t^{n}u(t)\) | \(\frac{n !}{s^{n+1}}\) | \(\mathbb{R}>0\) |
| \(−(t^{n}u(−t))\) | \(\frac{n !}{s^{n+1}}\) | \(\mathbb{R}<0\) |
| \(e^{-(\lambda t)} u(t)\) | \(\frac{1}{s+\lambda}\) | \(\mathbb{R}>-\lambda\) |
| \(-\left(e^{-(\lambda t)}\right) u(-t)\) | \(\frac{1}{s+\lambda}\) | \(\mathbb{R}<-\lambda\) |
| \(te^{-(\lambda t)}u(t)\) | \(\frac{1}{(s-\lambda)^{2}}\) | \(\mathbb{R}>-\lambda\) |
| \(t^{n} e^{-(\lambda t)} u(t)\) | \(\frac{n !}{(s+\lambda)^{n+1}}\) | \(\mathbb{R}>-\lambda\) |
| \(-\left(t^{n} e^{-(\lambda t)} u(-t)\right)\) | \(\frac{n !}{(s+\lambda)^{n+1}}\) | \(\mathbb{R}<-\lambda\) |
| \(\cos (bt) u(t)\) | \(\frac{s}{s^{2}+b^{2}}\) | \(\mathbb{R}>0\) |
| \(\sin (bt)u(t)\) | \(\frac{b}{s^{2}+b^{2}}\) | \(\mathbb{R}>0\) |
| \(e^{-(a t)} \cos (b t) u(t)\) | \(\frac{s+a}{(s+a)^{2}+b^{2}}\) | \(\mathbb{R}>-a\) |
| \(e^{-(a t)} \sin (b t) u(t)\) | \(\frac{b}{(s+a)^{2}+b^{2}}\) | \(\mathbb{R}>-a\) |
| \(\frac{d^{n}}{d t^{n}} \delta(t)\) | \(s^n\) | todos\(s\) |