# The necessities in DSP

## Discrete Fourier Transform

1. DFT Complex Phase (A.pdf, B.pdf)
2. DFT Matrix Examples (A.pdf, B.pdf)
3. DFT Matrix Properties (A.pdf, B.pdf)
4. DFT Frequency (A.pdf, B.pdf)
5. DFT Analysis (A.pdf, B.pdf)

## Types of Fourier Analysis

1. Overview of Fourier Analysis Types (A.pdf, B.pdf)
2. CTFS Analysis: Continuous Time Fourier Series (A.pdf, B.pdf)
3. CTFT Analysis: Continuous Time Fourier Transform (A.pdf, B.pdf)
4. DTFS Analysis: Discrete Time Fourier Series (A.pdf, B.pdf)
5. 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

Other Fourier Spectral Analysis

## 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

1. Nyquist Sampling  : Low-pass Signal Sampling (A.pdf, B.pdf)
2. Undersampling  : Band-pass Signal Sampling (A.pdf, B.pdf )
3. Oversampling (A.pdf, B.pdf)
4. Downsampling (A.pdf, B.pdf )
5. Upsampling (A.pdf, B.pdf )
6. Anti-aliasing Prefilters (A.pdf, B.pdf)
7. Anti-image Postfilters (A.pdf, B.pdf)
8. Sampler Spectra (A.pdf, B.pdf)
9. Reconstructor Spectra (A.pdf, B.pdf)
10. Quantization (A.pdf, B.pdf)

## The Role of Phase

1. Phase Delay and Group Delay (pdf)
2. All Pass Filter (pdf)
3. Minimum Phase System (pdf)

## Audio Signal Processing Experiments

1. Signal Generation (A.pdf, B.pdf)
2. Signal Analysis (A.pdf, B.pdf)
3. Signal Processing (A.pdf, B.pdf)

## Some Octave & GnuPlot Examples

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

## Mathematical Background

1. Complex Variables (A.pdf, B.pdf)
2. Hilbert Inner Product Space (pdf)
3. Hermitian Inner Product Space (pdf)
4. Laplace Transform (A.pdf, B.pdf)
5. 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

1. HW#3 (pdf)
2. HW#4 (pdf)
3. HW#5 (pdf)
4. HW#6 (pdf)
5. HW#7 (pdf)
6. HW#8 (pdf)
7. HW#9 (pdf)