Impulse invariance

Creator

Creator

Created

Created

2023 Nov 3 7:55

Editor

Editor

Edited

Edited

2023 Nov 30 16:54

Refs

Refs

Continuous to discrete means sampling

When we are given a desired CT system that we wish to implement is. If

H_c(j\Omega)

is band-limited (BL),

H_{eff}(j\Omega) = H_c(j\Omega) = H_c(j\omega/T) = H(e^{j\omega})

because of

FT of Impulse Train is

impulse train and

h[n] = h_c(nT)

(definition)

that’s FT is

H(e^{j\omega}) = \frac{1}{T} H_c(j\omega/T)

so we need to multiply

T

LPF

h[n] =\frac{sin(\pi n)}{\pi n}

Impulse invariance

Impulse invariance is a technique for designing discrete-time infinite-impulse-response (IIR) filters from continuous-time filters in which the impulse response of the continuous-time system is sampled to produce the impulse response of the discrete-time system. The frequency response of the discrete-time system will be a sum of shifted copies of the frequency response of the continuous-time system; if the continuous-time system is approximately band-limited to a frequency less than the Nyquist frequency of the sampling, then the frequency response of the discrete-time system will be approximately equal to it for frequencies below the Nyquist frequency.

Impulse invariance

https://en.wikipedia.org/wiki/Impulse_invariance

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