Transcript DSP-3 - Iran University of Science and Technology

Digital Signal
Processing
Electrical Engineering Department
Iran University of Science & Tech.
2/17/2007
DSP Course-IUST-Spring Semester
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Digital Signal Processing
Topic 3: Fourier domain
1. The Fourier domain
2. Discrete-Time Fourier Transform
(DTFT)
3. Discrete Fourier Transform (DFT)
4. Convolution with the DFT
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1. The Fourier Transform
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Fourier Series
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Fourier domain
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Fourier analysis
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Fourier analysis
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Fourier analysis
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sinc
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Fourier Analysis
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Fourier Transform
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Fourier Transform
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Fourier Transform of a sine
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Fourier Transforms
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2. Discrete Time FT (DTFT)
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DTFT
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Periodicity of DFT
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Inverse DTFT (IDTFT)
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IDTFT
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sinc again
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DTFTs of simple sequences
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DTFTs of simple sequences
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DTFTs of simple sequences
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DTFT properties
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DTFT example
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DTFT symmetry
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DTFT of real x[n]
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DTFT and convolution
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Convolution with DTFT
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DTFT convolution example
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DTFT modulation
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Parseval’s relation
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Energy density spectrum
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EDS and autocorrelation
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3. Discrete FT (DFT)
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DFT and IDFT
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IDFT
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DFT examples
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DFT: Matrix form
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Matrix IDFT
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DFT and DTFT
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DFT and MATLAB
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DTFT from DFT
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Periodic sinc
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Periodic sinc
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DFT from overlength DTFT
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DFT from overlength DTFT
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DFT from DTFT example
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DFT from DTFT example
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Properties: Circular time shift
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Circular time shift
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Circular time reversal
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4. Convolution with the DFT
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Circular convolution
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Circular convolution example
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Duality
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DFT properties summary
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Linear convolution w/ the DFT
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Linear convolution w/ the DFT
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Overlap-Add convolution
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Overlap-Add convolution
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