{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final_Tables - Table of Fourier Transform Pairs Signal Name...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Table of Fourier Transform Pairs Signal Name Time-Domain: x.t/ Frequency-Domain: X.j!/ Right-sided exponential e at u.t/ .a > 0/ 1 a C j! Left-sided exponential e bt u. t/ .b > 0/ 1 b j! Square pulse OEu.t C T=2/ u.t T=2/ sin .!T=2/ !=2 “sinc” function sin .! 0 t/ t OEu.! C ! 0 / u.! ! 0 / Impulse ı.t/ 1 Shifted impulse ı.t t 0 / e j!t 0 Complex exponential e j! 0 t 2 ı.! ! 0 / General cosine A cos .! 0 t C / Ae j ı.! ! 0 / C Ae j ı.! C ! 0 / Cosine cos .! 0 t/ ı.! ! 0 / C ı.! C ! 0 / Sine sin .! 0 t/ j ı.! ! 0 / C j ı.! C ! 0 / General periodic signal 1 X k D 1 a k e jk! 0 t 1 X k D 1 2 a k ı.! k! 0 / Impulse Train 1 X n D 1 ı.t nT / 2 T 1 X k D 1 ı.! 2 k=T / Table of Fourier Transform Properties Property Name Time-Domain x.t/ Frequency-Domain X.j!/ Linearity ax 1 .t/ C bx 2 .t/ aX 1 .j!/ C bX 2 .j!/ Conjugation x .t/ X . j!/ Time-Reversal x. t/ X. j!/ Scaling x.at/ 1 j a j X.j.!=a// Delay x.t t d / e j!t d X.j!/ Modulation x.t/e j! 0 t X.j.! ! 0 // Modulation x.t/ cos .! 0 t/ 1 2 X.j.! ! 0 // C 1 2 X.j.! C ! 0 // Differentiation d k x.t/ dt k .j!/ k X.j!/
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}