FT_Tables.pdf - Sec 5.2 Properties of the Fourier Transform 207 TABLE 5.1 Fourier Transform Properties Operation Time Function Fourier Transform

# FT_Tables.pdf - Sec 5.2 Properties of the Fourier Transform...

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Sec. 5.2 Properties of the Fourier Transform 207 TABLE 5.1 Fourier Transform Properties Operation Time Function Fourier Transform Linearity Time shift Time scaling Time transformation Duality Frequency shift Convolution Differentiation Integration 1 j v F ( v ) + p F (0) d ( v ) L t - q f ( t ) d t d n [ F ( v )] d v n ( - jt ) n f ( t ) ( j v ) n F ( v ) d n [ f ( t )] dt n 1 2 p F 1 ( v )* F 2 ( v ) f 1 ( t ) f 2 ( t ) F 1 ( v ) F 2 ( v ) f 1 ( t )* f 2 ( t ) F ( v - v 0 ) f ( t ) e j v 0 t 2 p f ( - v ) F ( t ) 1 ƒ a ƒ F ¢ v a e - j v t 0 / a f ( at - t 0 ) 1 ƒ a ƒ F ¢ v a f ( at ) F ( v ) e - j v t 0 f ( t - t 0 ) aF 1 ( v ) + bF 2 ( v ) af 1 ( t ) + bf 2 ( t ) then (5.10) where a and b are constants. In words, the principle of superposition applies to the Fourier transform. EXAMPLE 5.2 The linearity property of the Fourier transform We can make use of the property of linearity to find the Fourier transforms of some types of waveforms. For example, consider Using Euler’s relation, we can rewrite the expression for as f ( t ) = B 2 [ e j v 0 t + e - j v 0 t ] = B 2 e j v 0 t + B 2 e - j v 0 t .

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• Fall '17
• dr somaa
• Fourier Transform Properties

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