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ExtraHandout3 - 5.1 PROPERTIES OF THE BiSCRETE-TIME FOURtER...

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Unformatted text preview: 5.1 PROPERTIES OF THE BiSCRETE-TIME FOURtER TRANSFORM ‘ Property Aperiodic Signal Fourier Transform x[n] 3100)} periodic with fin] Kw } period 277 Linearity ‘ a.x[n] + by[n] _ aX_(w > + bYW f) Time Shifting x[n - no] V v ; ehlwn°X( w ) Frequency Shifting ej”°”x[n] . . X( 9“ ‘ WA) Conjugation x*[n] X'C‘ 00') Tune Reversal , xf—n] a XFUJJ . . , . x[n/k], if n = multiple of k T = ' me ExPansmn Min] { 0, if n #2 multiple of k ‘ X6200) Convolution x{n] * yin] XCOUJYCW J Multiplication xinlyin] 51;; X<.<9)Y(w - we "" 271' Differencng in Tme x[n] - x[n - 1] (1 '-‘ 6—”)3'903) 73 . , 1 Accumulanon kg” x[k] 1 __ eflw X ( w ) +0: - +ono ') Z 8(w - 277k) k: ~00 Differentiation in Frequency nx[n.] j £329) QdXCUD = GMXO' “5 )} 9m{X(w}} = ’9m{X(r 90‘) = X11:- OJ) Coniugate Symmetry for x[n] real ...
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This note was uploaded on 02/19/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue.

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ExtraHandout3 - 5.1 PROPERTIES OF THE BiSCRETE-TIME FOURtER...

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