Discrete-time Signal Process

주제무·2023년 1월 31일

DAE Lab

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23. 1. 30.

x = {x[n]}

if there is analog signal x_a, and x[n] are sample of the signal,
then

x[n] = x_a(nT)

refering to it as impulse

δ[n] = 0, n != 0 and 1, n = 0

any sequence can be expressed as

x[n] = Σ_k x[k] * δ[n-k]

power

P=\underset{T\rightarrow\infty}{lim} \dfrac{1}{T} \int_{-(T/2)}^{(T/2)} \lvert x(t) \lvert ^2 dt \ (Watts)

energy

E=\int_{-\infty}^\infty \lvert x(t) \lvert ^2 dt \ (Joules)

(f*g)(t) = \int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau