Digital Signal Processing

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Presentation transcript:

Digital Signal Processing Electrical Engineering Department Iran University of Science & Tech. 2/17/2007 DSP Course-IUST-Spring Semester

Digital Signal Processing Topic 3: Fourier domain 4/24/2017 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 2/17/2007 DSP Course-IUST-Spring Semester DSP Course Spring Semester Dr. Rezai-Rad

DSP Course-IUST-Spring Semester 1. The Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier Series 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier domain 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester sinc 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier Analysis 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

Fourier Transform of a sine 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Fourier Transforms 2/17/2007 DSP Course-IUST-Spring Semester

2. Discrete Time FT (DTFT) 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Periodicity of DFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Inverse DTFT (IDTFT) 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester IDTFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester sinc again 2/17/2007 DSP Course-IUST-Spring Semester

DTFTs of simple sequences 2/17/2007 DSP Course-IUST-Spring Semester

DTFTs of simple sequences 2/17/2007 DSP Course-IUST-Spring Semester

DTFTs of simple sequences 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT properties 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT symmetry 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT of real x[n] 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT and convolution 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Convolution with DTFT 2/17/2007 DSP Course-IUST-Spring Semester

DTFT convolution example 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT modulation 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Parseval’s relation 2/17/2007 DSP Course-IUST-Spring Semester

Energy density spectrum 2/17/2007 DSP Course-IUST-Spring Semester

EDS and autocorrelation 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester 3. Discrete FT (DFT) 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT and IDFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester IDFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT examples 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT: Matrix form 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Matrix IDFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT and DTFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT and MATLAB 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DTFT from DFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Periodic sinc 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Periodic sinc 2/17/2007 DSP Course-IUST-Spring Semester

DFT from overlength DTFT 2/17/2007 DSP Course-IUST-Spring Semester

DFT from overlength DTFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT from DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester DFT from DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

Properties: Circular time shift 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Circular time shift 2/17/2007 DSP Course-IUST-Spring Semester

Circular time reversal 2/17/2007 DSP Course-IUST-Spring Semester

4. Convolution with the DFT 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Circular convolution 2/17/2007 DSP Course-IUST-Spring Semester

Circular convolution example 2/17/2007 DSP Course-IUST-Spring Semester

DSP Course-IUST-Spring Semester Duality 2/17/2007 DSP Course-IUST-Spring Semester

DFT properties summary 2/17/2007 DSP Course-IUST-Spring Semester

Linear convolution w/ the DFT 2/17/2007 DSP Course-IUST-Spring Semester

Linear convolution w/ the DFT 2/17/2007 DSP Course-IUST-Spring Semester

Overlap-Add convolution 2/17/2007 DSP Course-IUST-Spring Semester

Overlap-Add convolution 2/17/2007 DSP Course-IUST-Spring Semester