convolution and DSP

convolution 摺積/捲積/疊積/旋積
convolution theorem 捲積定理

input: x[n]
system: h[n]
output: y[n]


convolution in time domain = multiplication in frequency domain

Time Domain:

y(n) = h(n) * x(n) = Σ h(k)x(n-k) where k ∈ Z (Z: integers 整數 ... -3, -2, -1, 0, 1, 2, 3, ...)

Frequency Domain:

Y(k) = H(k)X(k)

相關資料

Convolution (Wikipedia) / 摺積 (維基百科)
Video: Introduction to the convolution (Khan Academy 可汗學院)
Meaning of R, Q, Z, and N characters in math 數學中R, Q, Z, N的意義