# The necessities in DSP
## Discrete Fourier Transform

* DFT Complex Phase (A.pdf, B.pdf)
* DFT Matrix Examples (A.pdf, B.pdf)
* DFT Matrix Properties (A.pdf, B.pdf)
* DFT Frequency (A.pdf, B.pdf)
* DFT Analysis (A.pdf, B.pdf)

## Types of Fourier Analysis

* Overview of Fourier Analysis Types (A.pdf, B.pdf)
* CTFS Analysis: Continuous Time Fourier Series (A.pdf, B.pdf)
* CTFT Analysis: Continuous Time Fourier Transform (A.pdf, B.pdf)
* DTFS Analysis: Discrete Time Fourier Series (A.pdf, B.pdf)
* DTFT Analysis: Discrete Time Fourier Transform (A.pdf, B.pdf)

## Spectral Analysis

* Computational Aspect (A.pdf, B.pdf)
* Spectrum Representation (A.pdf, B.pdf)
* Spectral Leakage and Aliasing
* Smoothing and Windowing

## Example Octave Codes for Spectral Analysis

DFT Spectral Analysis
* Octave Codes for Digital Signals (A.pdf, B.pdf)
* Octave Codes for FFT Analysis (A.pdf, B.pdf)
Other Fourier Spectral Analysis
* Octave Codes for Utility Functions (A.pdf, B.pdf)
* Octave Codes for CTFS Analysis (A.pdf, B.pdf)
* Octave Codes for DTFS Analysis (A.pdf, B.pdf)
* Octave Codes for CTFT Analysis (A.pdf, B.pdf)
* Octave Codes for DTFT Analysis (A.pdf, B.pdf)

## Some Signal Functions
### Continuous Time Signal Functions

* The Sinusoidal Function (A.pdf, B.pdf)
* The Sinc Function (A.pdf, B.pdf)
* The Dirichlet Function (A.pdf, B.pdf)
* The Rectangle Function (A.pdf, B.pdf)
* The Impulse Function (A.pdf, B.pdf)
* Other Continuous Time Signal Functions (A.pdf, B.pdf)

### Discrete Time Signal Functions

* The Sinusoidal Function (A.pdf, B.pdf)
* The Sinc Function (A.pdf, B.pdf)
* The Dirichlet Function (A.pdf, B.pdf)
* The Rectangle Function (A.pdf, B.pdf)
* The Impulse Function (A.pdf, B.pdf)
* Other Discrete Time Signal Functions (A.pdf, B.pdf)

## Example Pairs of Fourier Analysis
### Continuous Time Pulse Functions

* Continuous Time Fourier Analysis Summary (A.pdf, B.pdf)
* CTFS of Periodic Pulse Functions (A.pdf, B.pdf)
* CTFT of Rectangular Pulse Functions (A.pdf, B.pdf)

### Discrete Time Pulse Functions

* Discrete Time Fourier Analysis Summary (A.pdf, B.pdf)
* DTFS of Periodic Pulse Functions (A.pdf, B.pdf)
* DTFT of Rectangular Pulse Functions (A.pdf, B.pdf)

## Sampling and Reconstruction

* Nyquist Sampling : Low-pass Signal Sampling (A.pdf, B.pdf)
* Undersampling : Band-pass Signal Sampling (A.pdf, B.pdf )
* Oversampling (A.pdf, B.pdf)
* Downsampling (A.pdf, B.pdf )
* Upsampling (A.pdf, B.pdf )
* Anti-aliasing Prefilters (A.pdf, B.pdf)
* Anti-image Postfilters (A.pdf, B.pdf)
* Sampler Spectra (A.pdf, B.pdf)
* Reconstructor Spectra (A.pdf, B.pdf)
* Quantization (A.pdf, B.pdf)

## The Role of Phase

* Phase Delay and Group Delay (pdf)
* All Pass Filter (pdf)
* Minimum Phase System (pdf)

## Audio Signal Processing Experiments

* Signal Generation (A.pdf, B.pdf)
* Signal Analysis (A.pdf, B.pdf)
* Signal Processing (A.pdf, B.pdf)

## Some Octave & GnuPlot Examples

* plot examples #1 (pdf)
* plot examples #2 (pdf)

## Mathematical Background

* Complex Variables (A.pdf, B.pdf)
* Hilbert Inner Product Space (pdf)
* Hermitian Inner Product Space (pdf)
* Laplace Transform (A.pdf, B.pdf)
* z Transform (A.pdf, B.pdf)

## Related Pages

DFT - Old
* 6.A DFT Complex Phase (pdf)
* 7.A DFT Matrix (pdf)
* 8.A DFT Analysis (pdf)
* 9.A DFT Frequency (pdf)
* 10.A FFT Analysis (pdf)
HW
* HW#3 (pdf)
* HW#4 (pdf)
* HW#5 (pdf)
* HW#6 (pdf)
* HW#7 (pdf)
* HW#8 (pdf)
* HW#9 (pdf)
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