# TableFT - Properties of the Fourier Transform Property t f...

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Unformatted text preview: Properties of the Fourier Transform Property ( ) t f ( ) ω F ___________________________________________________________________________ Linearity (Superposition) ( ) ( ) t f a t f a 2 2 1 1 + ( ) ( ) ω ω 2 2 1 1 F a F a + Time Shifting ( ) d t t f − ( ) ω ω F e d t j − Time Scaling ( ) ct f ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ c F c ω 1 Symmetry (Duality) ( ) t F ( ) ω π − f 2 Time Reversal ( ) t f − ( ) ω − F Frequency Scaling ( ) t j c e t f ω ( ) c F ω ω − Modulation ( ) ( ) t cos t f c ω ( ) ( ) c c F F ω ω ω ω + + − 2 1 2 1 Time Differentiation ( ) dt t df ( ) ω ω F j Frequency Differentiation ( ) t tf ( ) ω ω d dF j Conjugate ( ) t f * ( ) ω − * F Integration ( ) ∫ ∞ − t d f λ λ ( ) ( ) ( ) ω δ π ω ω 1 F F j + Convolution ( ) ( ) ∫ ∞ ∞ − − λ λ λ d t x h ( ) ( ) ω ω X H Multiplication ( ) ( ) t f t f 2 1 ( ) ( ) ∫ ∞ ∞ − − dv v F v F ω π 2 1 2 1 Parseval’s Theorem ( ) ∫ ∞ ∞ − dt t f 2 ( ) ∫ ∞ ∞ − ω...
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TableFT - Properties of the Fourier Transform Property t f...

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