The necessities in DSP

Discrete Fourier Transform Edit

  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 AnalysisEdit

  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 AnalysisEdit

  • 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 Edit

DFT Spectral Analysis

Other Fourier Spectral Analysis

Some Signal Functions Edit

Continuous Time Signal FunctionsEdit

Discrete Time Signal FunctionsEdit

Example Pairs of Fourier AnalysisEdit

Continuous Time Pulse FunctionsEdit

  • 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 FunctionsEdit

  • 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 ReconstructionEdit

  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 PhaseEdit

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

Audio Signal Processing ExperimentsEdit

  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 Edit

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

Mathematical BackgroundEdit

  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 Edit

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)


  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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