Discrete Fourier Transform
Why do we need another Fourier Representation? Fourier series represent signals as sums of sinusoids. They provide insights that are not obvious from time representations, but Fourier series only de ned for periodic signals. X[k] = X n=hNi x[n]e−j2πkn/N (summed over a period) Fourier transforms have no periodicity constaint: X(Ω) = X∞ n ...
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Impulse Response and Convolution
sigproc.mit.eduImpulse Response If a system is linear and time-invariant (LTI), its input-output relation is completely speci ed by the system’s impulse response h(t). 1. One can always nd the impulse response of a system. δ (t)system h 2. Time invariance implies that shifting the input simply shifts the output. δ (t−τ)system h 3.
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