The necessities in DSP

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Discrete Fourier Transform [edit | edit source]

  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[edit | edit source]

  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[edit | edit source]

  • 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 | edit source]

DFT Spectral Analysis

Other Fourier Spectral Analysis


Some Signal Functions [edit | edit source]

Continuous Time Signal Functions[edit | edit source]

Discrete Time Signal Functions[edit | edit source]


Example Pairs of Fourier Analysis[edit | edit source]

Continuous Time Pulse Functions[edit | edit source]

  • 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[edit | edit source]

  • 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[edit | edit source]

  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[edit | edit source]

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


Audio Signal Processing Experiments[edit | edit source]

  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 | edit source]

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


Mathematical Background[edit | edit source]

  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 | edit source]



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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