Linear Time-Invariant (LTI) system 線性非時變系統

linear time-invariant system/LTI system 線性非時變系統

linearity 線性
input 和 output 間呈線性的對應關係

time-invariance 非時變性
當 input 在時間上有延遲時，output 也會有相同的延遲

因果線性非時變系統：
h(n) = 0, n < 0

A LTI system may be represented using the following equations with constant coefficients:
Differential Equation 微分方程式 (Continuous-Time)
Difference Equation 差分方程式 (Discrete-Time) e.g. y[n] = Σa_kx[n-k] + Σb_ky[n-k]

An LTI system has an impulse response of h(t). The output of the system y(t) can be obtained using the convolution of the input x(t) and the impulse response h(t):

y(t) = x(t) * h(t)

y[n] = x[n] * h[n]

In the frequency domain, the convolution sign * is replaced by the '·' sign for multiplication.

Y(ω) = X(ω) · H(ω)

Therefore, an LTI system convolutes the input signal with the system's impulse response in the time domain.

相關資訊

LTI system theory (Wikipedia)