CTFS Conjugate

Creator

Created

2023 Oct 7 6:31

Editor

Edited

2023 Oct 10 5:9

Refs

x(t) \xleftrightarrow{FS} a_k

x(t)^\ast \xleftrightarrow{FS} a_{-k}^\ast

If x is real → $a_{-k} = a_k^\ast$ → $|a_{-k}| = |a_k|$ (absolute value is $\sqrt{a^2 + b^2}$ when $a +bj$ )

If x is real and even → $a_k = a_{-k} = a_k^\ast$ →
Fourier coefficient are real and even

If x is real and odd → $a_k = -a_{-k} = -a_k^\ast$ →
Fourier coefficient are purely imaginary and odd

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