Pares DFT
Referencia: McClellan Tabla 8.1 p327-328
| x[n] | X[k] |
|---|---|
| δ[n] | 1 |
| δ[n-nd] | e^{-j(2\pi k/N)n_d} |
| r_L[n] = \mu [n] - \mu [n-L] | \frac{\sin\Big(\frac{1}{2}L(2\pi k/N)\Big)}{\sin\Big(\frac{1}{2}(2\pi k/N)\Big)}e^{-j(2\pi k/N)(L-1)/2} |
| D_L(2\pi k/N) = \frac{\sin\Big(\frac{1}{2}L(2\pi k/N)\Big)}{\sin\Big(\frac{1}{2}(2\pi k/N)\Big)} | |
| r_L[n] e^{j(2\pi k_0/N)n} | D_L(2 \pi (k-k0)/N)e^{-j(2\pi (k-k_0)/N)(L-1)/2} |
DFT Propiedades
| Propiedad | dominio tiempo x[n] | dominio frecuencia X[k] |
|---|---|---|
| Periódica | x[n] = x[n+N] | X[k] = X[k+N] |
| Linealidad | ax1[n] +bx2[n] | aX1[k] +bX2[k] |
| Simetría Conjugada | x[n] Real | X[N-k] = x*[k] |
| Conjugación | x*[n] | X*[N-K] |
| Reversible en tiempo | x[ ((N-n))N ] | X[N-k] |
| Retraso | x[ ((n-nd))N ] | e^{ -j (2\pi k/N)n_d} X[k] |
| Desplazamiento en frecuencia | x[n] e^{ j (2\pi k_0/N)n} | X[k-k0] |
| Modulación | x[n] \cos\Big((2π k_0/N)n\Big) | \frac{1}{2}X[k-k_0] + \frac{1}{2}X[k+k_0] |
| Convolución | \sum_{m=0}^{N-1} h[m]x[((n-m))_N ] | H[k]X[k] |
| Teorema de Parseval | \sum_{n=0}^{N-1} |x[n]|^2 = \frac{1}{N}\sum_{k=0}^{N-1} |X[k]|^2 | |