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StackExchange Answers

DOI

"Watch" to be notified of new posts.

Question titles may be paraphrased, but IDs are exact.

Citing

If using significant portions of code, please cite this repository. Short form (year = latest, or when the cited content was published):

John Muradeli, StackExchange Answers, 2023. GitHub repository, https://github.com/OverLordGoldDragon/StackExchangeAnswers/. DOI: 10.5281/zenodo.5115534

BibTeX

@article{OverLordGoldDragon2020StackExchangeAnswers,
  title={StackExchange Answers},
  author={John Muradeli},
  journal={GitHub. Note: https://github.com/OverLordGoldDragon/StackExchangeAnswers/},
  year={2023},
  doi={10.5281/zenodo.5115534},
}

Signal Processing / Feature Engineering

Code-accompanied answers say "code Q...", found in respective folders, or "code included".

✯ = exceptional quality; 🡡 = great quality (brag!)

Feature Engineering (applied) / Problem Solving

  1. ✯ Identifying abrupt changes in audio - Q&A, code Q87355
  2. 🡡 Locating non-homogeneous areas in an image - Q&A, code included
  3. 🡡 Estimate sine frequency under white noise - Q&A, code Q76644
  4. Extract sine phase and amplitude, accurate and noise-robust method - Q&A, code Q29509
  5. Nonlinear filtering and inspection of noisy vibration signal - Q&A, code included

Intuition / "Deep" Explanations

  1. ✯ Physical significance of negative frequencies - Q&A
  2. ✯ Wavelet "center frequency" explanation, relation to CWT scales - Q&A, code Q76329
  3. 🡡 DFT coefficients meaning? - Q&A
  4. 🡡 Why is |x|^2 power? - Q&A
  5. 🡡 Does zero-padding distort the spectrum? - Q&A
  6. How is a 1D signal considered a "vector"? - Q&A
  7. Are colored images 2D or 3D? - Q&A
  8. Are real-world signals bandlimited? - Q&A
  9. What can be meant by "bandlimited"? - Q&A

Measures / Heuristics

  1. ✯ How to validate a wavelet filterbank? - Q&A, code to-be-released
  2. 🡡 How to measure aliasing? - Q&A, code Q87705

Time-Frequency Analysis / Feature Engineering

  1. ✯ Wavelet Scattering explanation - Q&A, code Q78512
  2. ✯ Joint Time-Frequency Scattering explanation - Q&A, code Q78644
  3. ✯ Synchrosqueezing explanation - Q&A
  4. ✯ Wavelet Scattering properties & implementation - Q&A, code Q78512
  5. 🡡 Equivalence between "windowed Fourier transform" and STFT as convolutions/filtering - Q&A, code Q86937
  6. 🡡 What is "spin" for the 2D (separable) Morlet? - Q&A, code to-be-released
  7. 🡡 Amplitude extraction using STFT - Q&A, code Q86726
  8. 🡡 Why are there beats in STFT of sines? - Q&A, code Q11333
  9. 🡡 Power/Energy from CWT - Q&A, code Q86181
  10. 🡡 CWT vs DWT - Q&A
  11. 🡡 One-integral inverse CWT - Q&A, code included
  12. 🡡 Joint Time-Frequency Scattering structure & implementation - Q&A, code Q78644
  13. What do CWT values correspond to? - Q&A, code included
  14. Role of window length and overlap in uncertainty principle - Q&A, Q80918
  15. Inverting a scalogram - Q&A, code Q78530
  16. Importance of overlap in STFT - Q&A
  17. Advantages of complex wavelets over real-valued - Q&A
  18. Bandpass filtering for amplitude - Q&A, code included
  19. How is wavelet time & frequency resolution computed? - Q&A
  20. How is wavelet center frequency computed? - Q&A

Signal Theory

  1. ✯ DFT of a sine, closed form solution and insights - Q&A, code Q87926
  2. 🡡 Subsampling in frequency domain, Effect of sampling rate on spectrum - Q&A, code included
  3. 🡡 Why is SNR periodic/sinusoidal for streamed windowing of a sine? - Q&A
  4. 🡡 DFT modulus of a sine, closed form solution and insights - Q&A, code Q87926
  5. Relationship between energy, power, and sampling rate - Q&A, code Q85745
  6. Hilbert transform for amplitude extraction/demodulation of broadband waveforms - Q&A
  7. Other end of Nyquist limit - Q&A
  8. Instantaneous frequency of a signal - Q&A
  9. DFT filter bank interpretation - Q&A
  10. ifft first half of time domain ("DFT unpad property") - Q&A, code included
  11. Role of padding in convolution / Alleviating edge effects in Hilbert transform - Q&A, code Q76754
  12. How to frequency modulate? - Q&A
  13. Symmetries of analyticity - Q&A
  14. Effect of sampling rate and duration on discrete parameters of sine (spectrum) - Q&A

Algorithms

  1. 🡡 2D FFT cross-correlation in Python - Q&A, code Q87781
  2. Efficient 2D convolution/cross-correlation along only one axis (1D output) - Q&A, code included
  3. Optimizing window length in STFT via gradient descent - Q&A, code Q81624

Proofs / Mathy

  1. 🡡 Amplitude extraction / demodulation criteria for Hilbert transform - Q&A
  2. 🡡 Is downsampling LTI for bandlimited inputs? - Q&A, code Q88042
  3. 🡡 Sine DFT: N/4-symmetry, bin sinusoidal modulation vs time shifts - Q&A, code Q87926
  4. Inverse CWT derivation - Q&A

License

MIT-licensed.