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Unformatted text preview: Fourier Transform
• For non-periodic signals
• Sufficient conditions
– ∞ – Finite discontinuities • Convert time domain to frequency domain
– Similar to Laplace transform ME365 Spectrum Analysis 1 Fourier Transform
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
– 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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This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue University-West Lafayette.
- Fall '07