离散信号卷积公式表大全

离散信号卷积公式表大全
离散信号卷积公式大全
1. 离散时间序列的卷积：
x(n) * h(n) = y(n) = sum (xK * hn - K, for k=-∞ to k =∞)
2. 非时域的常规卷积：
x(m,n) * h(m,n) = y(m,n) = sum (xK,L * hm - K, n - L, for k=-∞ to k =∞ ,l=-∞ to l=∞)
3. 离散二维卷积：
x(m,n) * h(m,n) = (x⊗h)(m,n) = sum (xk-m,l-n * hk,l ,for k=-∞ to k =∞ ,l=-∞ to l=∞)
4. 重叠窗口卷积：
y(n) = sum (xk * hn-k ,for k=0 to k=N-1)
5. 开放式卷积：
y(n) = x(n) * h(n) = sum ( xk * hn-k, for k=1 to k=∞)
6. 闭放式卷积：
y(n) = x(n) * h(n) = sum (xk * hn-k , for k=1 to k=M)
7. 部分卷积：
y(n) = x(n) * h(n) = sum ( xk * hn-k , for k=1 to k=M)
8. 时域有限卷积：
y(n) = x(n) * h(n) = sum(xk * hn-k,for k=0 to k=N-1)
9. 周期卷积：
y(n) = x(n) * h(n) = sum (xk * hn-k (mod periodicX), for k=0 to k=N-1)
10. 周期有限卷积：
y(n) = x(n) * h(n) = sum (xk * hn-k (mod periodicX), for k=0 to k=N-1)
11. 环形有限卷积：
y(n) = x(n) * h(n) = sum (xk * hn-k (mod2N), for k=0 to k=N-1)
12. 便携因子卷积：
y(n) = x(n) * h(n) = sum (xj * hn+j, for j=0 to j=N-1)
13. 周期有限卷积：
y(n) = x(n) * h(n) = sum (xk * hn-k (mod periodicX), for k=0 to k=N-1)
14. 直接牛顿方法卷积：
y[n] = x * h * FOR (k=-N/2 ; k=N/2 ; k++) {x(k) * h(-n-k)
15. 快速傅利叶变换卷积：
y[n] = x[n] * h[n] = sum (X(K) * H(-n - K) ,for k=0 to k=N-1)。