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DTFT_Properties

DTFT_Properties - 5.1 PROPERTIES OF THE DISCRETE-TIME...

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Unformatted text preview: 5.1 PROPERTIES OF THE DISCRETE-TIME FOURIER TRANSFORM Property Aperiodic Signal Fourier Transform fin] X( cu )} periodic with y[n] Y( CL) } period 277' Linearity ax[n] + by[n] aXCW ) + 1717“") T) Time Shifting x9: ~ no] e“""”‘°X{ w ) Frequency Shifting ej”°”x[n] X( W " wg) Conjugation x*[n] X’C‘ 03") Tune Reversal xi—n] . X ( 400 J , . .. . __ xD‘Z/k}, if n == multiple of k _ Tune Expansmn Min] _ { 0, if :2 # multiple of k ‘ X0200) Convolution x92] * yin] XCWWCW J Multiplication xfnbvin] 317-2: X(.C9)Y(W ‘ (9)519 ”' 277 ‘Differencing in Tme x[n] — xfn ~ 1] (1 “-‘ 3—1;”)?{6'05} . .” 1 Accumulanon 1;.” xfk] 1 __ fig, X ( w ) +¢rX(¢O") Z 8(w - 277k) . k: -oa Difierentiation in Frequency min] f d???) Km); = XV?- 09) (Rd-7500)} = (Re{X(-— “3 )} Cmiugate Symmetry for x[n] real 9m{X(vw)} = “327%{XG‘ w?) ...
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