D02 - BIEN 130: Bioinstrumentation D02 May 6, 2009 Hyle...

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Unformatted text preview: BIEN 130: Bioinstrumentation D02 May 6, 2009 Hyle Park Fourier transforms Complex numbers Definition The point of Fourier transforms is to identify what frequency components make up any particular function cos sin jx e x i x = + ( 29 ( 29 ( 29 1 2 j t v t v t e dt V - = = ( 29 ( 29 ( 29 1 1 2 j t V V e d v t - = = Fourier transform pairs Common examples identity Complex exponential Cosine Sine Gaussian ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 1 2 2 2 1 2 2 cos sin t j t j t v t V v t e dt e t t j e e ---- =- + +- +-- Fourier transform properties Useful rules Reversibility Linearity Scaling Shifting Frequency shifting ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 2 1 1 2 2 1 2 1 j t a a j t j t v t V v t e dt...
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D02 - BIEN 130: Bioinstrumentation D02 May 6, 2009 Hyle...

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