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lec22_handout - Fourier Transform • For non-periodic...

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Unformatted text preview: Fourier Transform • For non-periodic signals • Sufficient conditions – ∞ – Finite discontinuities • Convert time domain to frequency domain – to – Similar to Laplace transform ME365 Spectrum Analysis 1 Fourier Transform T A -d/2 d/2 • Even function 2 2 cos • Compare Ak to A0 2 sin sin ⋅ sin 2 2 ME365 Spectrum Analysis 2 Fourier Transform • Plot the spectrum – Spacing between points depends on T – As → ∞, spectrum plot becomes continuous ME365 Spectrum Analysis 3 Fourier Transform • Width of the first lobe depends on d – As → 0, bandwidth needed increases ME365 Spectrum Analysis 4 Fourier Transform • Converting time-domain to frequency-domain • Converting frequency-domain to time-domain • But is this integral an efficient use of your time? • Use Discrete Fourier Transform (DFT) ME365 Spectrum Analysis 5 Discrete Fourier Transform • Continuous time signal sampled at Δ Δ • DFT implemented with Fast Fourier Transform (FFT) – May require length of input vector to be a power of 2 – MATLAB does not require this, but it is faster – Consult the manual for your specific implementation ME365 Spectrum Analysis 6 ...
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