fourier_transform_review

fourier_transform_review - Review of Continuous‐time...

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Unformatted text preview: Review of Continuous‐time Fourier Transform 1. Continuous‐time Fourier transform of aperiodic signals , 2. Properties of continuous‐time Fourier transform • • Linearity: if . Shifting property: if o • o Convolution property: if o o • Symmetry: if , then , o o If x(t) is real, then o If x(t) is real and symmetric symmetric . and . is conjugate symmetric. , then . is also real and and y , then and and h , then and , then for all real numbers a and b, 1 2 3. Continuous‐time Fourier transform pairs for elementary continuous‐time signals Signals Constant Unit impulse signal Causal decaying exponential signal Two‐sided decaying exponential signal Complex exponential Cosine signal Sine signal Rectangular signal Sinc signal Impulse train 1, | | 0, | | Time domain 1 || Frequency domain 2 1 1 2 2 ) ) Comments a>0 a>0 cos sin * ** , 1, 2 0 0 ** 2 2 * ...
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