The necessities in DSP

Discrete Fourier Transform

 * 1) DFT Complex Phase ([[Media:DFT.1.A.Complex_Phase.20110511.pdf |A.pdf]], [[Media:DFT.1.B.Complex Phase.pdf |B.pdf]])
 * 2) DFT Matrix Examples ([[Media:DFT.2.A.Matrix_Example.20110511.pdf |A.pdf]], [[Media:DFT.2.B.Matrix Example.20120208.pdf |B.pdf]])
 * 3) DFT Matrix Properties ([[Media:DFT.3.A.Matrix_Property.20110514.pdf |A.pdf]], [[Media:DFT.3.B.Matrix_Property.20111214.pdf |B.pdf]])
 * 4) DFT Frequency ([[Media:DFT.4.A.Frequency.20110516.pdf |A.pdf]], [[Media:DFT.4.B.Frequency.20110516.pdf |B.pdf]])
 * 5) DFT Analysis ([[Media:DFT.5.A.Analysis.20180131.pdf |A.pdf]], [[Media:DFT.5.B.Analysis.20180131.pdf |B.pdf]])

Types of Fourier Analysis

 * 1) Overview of Fourier Analysis Types ([[Media:Fourier.0.A.Overview.20161212.pdf |A.pdf]], [[Media:Fourier.0.B.Overview.20161209.pdf |B.pdf]])
 * 2) CTFS Analysis: Continuous Time Fourier Series  ([[Media:Fourier.1.A.CTFS.20160809.pdf |A.pdf]], [[Media:Fourier.1.B.CTFS.20160812.pdf |B.pdf]])
 * 3) CTFT Analysis: Continuous Time Fourier Transform ([[Media:2.A.CTFT.20160820.pdf |A.pdf]], [[Media:Fourier.2.B.CTFT.20160827.pdf |B.pdf]])
 * 4) DTFS Analysis: Discrete Time Fourier Series  ([[Media:Fourier.3.A.DTFS.20160816.pdf |A.pdf]], [[Media:Fourier.3.B.DTFS.20160820.pdf |B.pdf]])
 * 5) DTFT Analysis: Discrete Time Fourier Transform ([[Media:Fourier.4.A.DTFT.20160820.pdf |A.pdf]], [[Media:Fourier.4.B.DTFT.20160820.pdf |B.pdf]])

Spectral Analysis

 * Computational Aspect ([[Media:Spectrum.1.A.Compute.20170114.pdf |A.pdf]], [[Media:Spectrum.1.B.Compute.20170114.pdf |B.pdf]])
 * Spectrum Representation ([[Media:Spectrum.2.A.Represent.20170102.pdf |A.pdf]], [[Media:Spectrum.2.B.Represent.20170123.pdf |B.pdf]])
 * Spectral Leakage and Aliasing
 * Smoothing and Windowing

Example Octave Codes for Spectral Analysis
DFT Spectral Analysis
 * Octave Codes for Digital Signals ([[Media:Octave.DFT.0.A.DSig.20180101.pdf |A.pdf]], [[Media:Octave.DFT.0.B.DSig.20170807.pdf |B.pdf]])
 * Octave Codes for FFT Analysis ([[Media:Octave.DFT.1.A.FFT.20170706.pdf |A.pdf]], [[Media:Octave.DFT.1.B.FFT.20170706.pdf |B.pdf]])

Other Fourier Spectral Analysis
 * Octave Codes for Utility Functions ([[Media:Octave.0.A.Util.20180124.pdf |A.pdf]], [[Media:Octave.0.B.Util.20180201.pdf |B.pdf]])
 * Octave Codes for CTFS Analysis ([[Media:Octave.1.A.CTFS.20180110.pdf |A.pdf]], [[Media:Octave.1.B.CTFS.2017.pdf |B.pdf]])
 * Octave Codes for DTFS Analysis ([[Media:Octave.2.A.DTFS.20180117.pdf |A.pdf]], [[Media:Octave.2.B.CTFS.2017.pdf |B.pdf]])
 * Octave Codes for CTFT Analysis ([[Media:Octave.3.A.CTFT.20180117.pdf |A.pdf]], [[Media:Octave.3.B.CTFS.2017.pdf |B.pdf]])
 * Octave Codes for DTFT Analysis ([[Media:Octave.4.A.DTFT.20180118.pdf |A.pdf]], [[Media:Octave.4.B.CTFS.2017.pdf |B.pdf]])

Continuous Time Signal Functions

 * The Sinusoidal Function ([[Media:SFunc.CT.0.A.Sinusoid000.pdf |A.pdf]], [[Media:SFunc.CT.0.B.Sinusoid.20131005.pdf |B.pdf]])
 * The Sinc Function ([[Media:SFunc.CT.1.A.Sinc.pdf |A.pdf]], [[Media:SFunc.CT.1.B.Sinc.20131102.pdf |B.pdf]])
 * The Dirichlet Function ([[Media:SFunc.CT.2.A.Dirichlet.pdf |A.pdf]], [[Media:SFunc.CT.2.B.Dirichlet.20130610.pdf |B.pdf]])
 * The Rectangle Function ([[Media:SFunc.CT.3.A.Rect.pdf |A.pdf]], [[Media:SFunc.CT.3.B.Rect.20130610.pdf |B.pdf]])
 * The Impulse Function ([[Media:SFunc.CT.4.A.Impulse.pdf |A.pdf]], [[Media:SFunc.CT.4.B.Impulse.20130625.pdf |B.pdf]])
 * Other Continuous Time Signal Functions ([[Media:SFunc.CT.5.A.other.pdf |A.pdf]], [[Media:SFunc.CT.5.B.other.pdf |B.pdf]])

Discrete Time Signal Functions

 * The Sinusoidal Function ([[Media:SFunc.DT.0.A.Sinusoid.pdf |A.pdf]], [[Media:SFunc.DT.0.B.Sinusoid.20130926.pdf |B.pdf]])
 * The Sinc Function ([[Media:SFunc.DT.1.A.Sinc.pdf |A.pdf]], [[Media:SFunc.DT.1.B.Sinc.20130926.pdf |B.pdf]])
 * The Dirichlet Function ([[Media:SFunc.DT.2.A.Dirichlet.pdf |A.pdf]], [[Media:SFunc.DT.2.B.Dirichlet.pdf |B.pdf]])
 * The Rectangle Function ([[Media:SFunc.DT.3.A.Rect.pdf |A.pdf]], [[Media:SFunc.DT.3.B.Rect.20130813.pdf |B.pdf]])
 * The Impulse Function ([[Media:SFunc.DT.4.A.Impulse.pdf |A.pdf]], [[Media:SFunc.DT.4.B.Impulse.20130817.pdf |B.pdf]])
 * Other Discrete Time Signal Functions ([[Media:SFunc.5.A.other.pdf |A.pdf]], [[Media:SFunc.5.B.other.pdf |B.pdf]])

Continuous Time Pulse Functions

 * Continuous Time Fourier Analysis Summary ([[Media:FPairs.CT.1.A.Pulse.pdf |A.pdf]],  [[Media:FPairs.CT.1.B.Pulse.20130706.pdf |B.pdf]])
 * CTFS of Periodic Pulse Functions ([[Media:FPairs.CT.2.A.Pulse.CTFS.pdf |A.pdf]],  [[Media:FPairs.CT.2.B.Pulse.CTFS.20130711-2.pdf |B.pdf]])
 * CTFT of Rectangular Pulse Functions ([[Media:FPairs.CT.3.A.Pulse.CTFT.pdf |A.pdf]],  [[Media:FPairs.CT.3.B.Pulse.CTFT.20131109.pdf |B.pdf]])

Discrete Time Pulse Functions

 * Discrete Time Fourier Analysis Summary ([[Media:FPairs.DT.1.A.Pulse.pdf |A.pdf]],  [[Media:FPairs.DT.1.B.Pulse.20130610.pdf |B.pdf]])
 * DTFS of Periodic Pulse Functions ([[Media:FPairs.DT.2.A.Pulse.DTFS.pdf |A.pdf]],  [[Media:FPairs.DT.2.B.Pulse.DTFS.20130610.pdf |B.pdf]])
 * DTFT of Rectangular Pulse Functions ([[Media:FPairs.DT.3.A.Pulse.DTFT.pdf |A.pdf]],  [[Media:FPairs.DT.3.B.Pulse.DTFT.20130805.pdf |B.pdf]])

Sampling and Reconstruction

 * 1) Nyquist Sampling  : Low-pass Signal Sampling    ([[Media:Sampling.1.A.Basics.20130907.pdf |A.pdf]], [[Media:Sampling.1.B.Basics.20131005.pdf |B.pdf]])
 * 2) Undersampling  : Band-pass Signal Sampling   ([[Media:Sampling.2.A.Under.20120404.pdf |A.pdf]], [[Media:Sampling.2.B.Under.20120404.pdf |B.pdf]] )
 * 3) Oversampling  ([[Media:Sampling.3.A.Over.pdf |A.pdf]], [[Media:Sampling.3.B.Over.20120712.pdf |B.pdf]])
 * 4) Downsampling  ([[Media:Sampling.4.A.Down.pdf |A.pdf]], [[Media:Sampling.4.B.Down.20121115.pdf |B.pdf]] )
 * 5) Upsampling  ([[Media:Sampling.5.A.pdf |A.pdf]], [[Media:Sampling.5.B.Up.20121115.pdf |B.pdf]] )
 * 6) Anti-aliasing Prefilters ([[Media:Sampling.6.A.pdf |A.pdf]], [[Media:Sampling.6.B.Prefilter.20120727.pdf |B.pdf]])
 * 7) Anti-image Postfilters ([[Media:Sampling.7.A.pdf |A.pdf]], [[Media:Sampling.7.B.Postfilter.20120727.pdf |B.pdf]])
 * 8) Sampler Spectra  ([[Media:Sampling.8.A.Sampler.pdf |A.pdf]], [[Media:Sampling.8.B.Sampler.20120623.pdf |B.pdf]])
 * 9) Reconstructor Spectra ([[Media:Sampling.9.A.Reconstructor.pdf |A.pdf]], [[Media:Sampling.9.B.Reconstructor.20120629.pdf |B.pdf]])
 * 10) Quantization ([[Media:Sampling.10.A.Quantization.pdf |A.pdf]], [[Media:Sampling.10.B.Quantization.20130912.pdf |B.pdf]])

The Role of Phase

 * 1) Phase Delay and Group Delay ([[Media:Misc.1.A.GroupPhase.20120719.pdf |pdf]])
 * 2) All Pass Filter ([[Media:Misc.2.A.AllPass.20120813.pdf |pdf]])
 * 3) Minimum Phase System ([[Media:Misc.3.A.MinPhase.20120813.pdf |pdf]])

Audio Signal Processing Experiments

 * 1) Signal Generation ([[Media:Audio.1.SigGen.1.A.20180122.pdf |A.pdf]], [[Media:Audio.1.SigGen.1.B.20180202.pdf |B.pdf]])
 * 2) Signal Analysis ([[Media:Audio.2.SigAnal.1.A.20180217.pdf |A.pdf]], [[Media:Audio.2.SigAnal.1.B.20180210.pdf |B.pdf]])
 * 3) Signal Processing ([[Media:Audio.3.SigProc.1.A.20180119.pdf |A.pdf]], [[Media:Audio.3.SigProc.1.B.20180406.pdf |B.pdf]])

Some Octave & GnuPlot Examples

 * 1) plot examples #1 ([[Media:plot.20140528.pdf |pdf]])
 * 2) plot examples #2 ([[Media:plot2.20140528.pdf |pdf]])

Mathematical Background

 * 1) Complex Variables ([[Media:DFT.0.A.Background.pdf |A.pdf]], [[Media:DFT.0.B.Background.pdf |B.pdf]])
 * 2) Hilbert Inner Product Space ([[Media:Math.2.B.Hilbert.20120223.pdf |pdf]])
 * 3) Hermitian Inner Product Space ([[Media:Math.3.B.Hermitian.20120209.pdf |pdf]])
 * 4) Laplace Transform  ([[Media:Math.4.A.Laplace.20121207.pdf |A.pdf]], [[Media:Math.4.B.Laplace.20121214.pdf |B.pdf]])
 * 5) z Transform ([[Media:Math.5.A.zTransform.pdf |A.pdf]], [[Media:Math.5.B.zTransform.20130226.pdf |B.pdf]])

Related Pages
DFT - Old
 * 6.A DFT Complex Phase ([[Media:6.A.DFT Complex Phase.pdf |pdf]])
 * 7.A DFT Matrix ([[Media:7.A.DFT Matrix.pdf |pdf]])
 * 8.A DFT Analysis ([[Media:8.A.DFT Analysis.pdf |pdf]])
 * 9.A DFT Frequency ([[Media:9.A.DFT Frequency.pdf |pdf]])
 * 10.A FFT Analysis ([[Media:9.A.FFT.pdf |pdf]])

 HW
 * 1) HW#3 ([[Media:HW03.pdf |pdf]])
 * 2) HW#4 ([[Media:DSP_HW04.pdf |pdf]])
 * 3) HW#5 ([[Media:DSP_HW05.pdf |pdf]])
 * 4) HW#6 ([[Media:DSP_HW06.pdf |pdf]])
 * 5) HW#7 ([[Media:DSP_HW07.20111005.pdf |pdf]])
 * 6) HW#8 ([[Media:DSP_HW08.pdf |pdf]])
 * 7) HW#9 ([[Media:DSP_HW09.pdf |pdf]])

go to [ Electrical_%26_Computer_Engineering_Studies ]