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

• 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

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)

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