Signal Processing
Signal Processing
Signal Processing
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Transform theory<br />
Important symmetry properties of the Discrete Fourier Transform (DFT)<br />
˜x n real ⇔ ˜X k = ˜X ∗ −k = ˜X ∗ N−k ⇔ { | ˜Xk | = | ˜X −k | = | ˜X N−k |<br />
arg ˜X k = − arg ˜X −k = − arg ˜X N−k<br />
Proof: Similar as above.<br />
˜X k real ⇔ ˜x n = ˜x ∗ −n = ˜x∗ N−n<br />
Sven Nordebo, School of Computer Science, Physics and Mathematics, Linnæus University, Sweden. 28(28)
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