CHAPTER 3 PART 2 FOURIER TRANSFORM PROPERTIES.pdf - 1 FOURIER TRANSFORM PROPERTIES 2 Linearity(superposition Time shift Time scale Duality Frequency

CHAPTER 3 PART 2 FOURIER TRANSFORM PROPERTIES.pdf - 1...

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FOURIER TRANSFORM PROPERTIES 2 Linearity (superposition) Time shift Time scale Duality Frequency shift (Modulation) Convolution Differentiation
LINEARITY @ SUPERPOSITION
Solution: Example : Find the Fourier Transform for the signal ) ( ) ( 3 3 ) ( 2 2 2 t u e t u e e t f t t t From Table C.2: j t u e t 2 1 ) ( 2 j t u e t 2 1 ) ( 2 2 2 4 12 4 ) 2 )( 2 ( 3 2 1 2 1 3 ) ( j j F t e 2 3 j a A t u Ae at ) (
Example : Find the Fourier Transform for the signal g(t) ) 2 ( ) 6 ( 5 . 0 ) ( ) ( ) ( : 2 1 t rect t rect t g t g t g Solution ) ( sin 2 ) 3 ( sin 3 ) ( ) ( ) ( : 2 1 c c G G G Transform Fourier In v(t) A - t /2 t /2 t 2 sin ) ( t t c A V t t Arect t v ) (
Time delay of a signal causes a linear phase shift in the spectrum of the signal. If the signal is delayed by , the phase spectrum will be shifted by . The amplitude remains the same TIME SHIFT 0 ) ( ) ( ) ( ) ( 0 t j e V t t v V t v 0 t 0 t
Example : Find the Fourier Transform for the signal Solution: 2 / 2 | 5 . 0 | 2 4 12 3 j t e e 5 . 0 2 3 t e

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