CTFS Time operation

Creator

Creator

Created

Created

2023 Oct 7 6:23

Editor

Editor

Edited

Edited

2023 Oct 10 4:42

Refs

Refs

Time Shift

Magnitude unchanging is important property

x(t) \xleftrightarrow{FS} a_k \text{, }x(t - t_0) \xleftrightarrow{FS} e^{-jk\omega_0t_0}a_k

easy to show using

Fourier coefficient definition

Time scaling

x(\alpha t) = \sum_ka_ke^{jk(\alpha \omega_0) t}

with period

T/\alpha

and

a_k

remains unchanged

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