StackExchange Answers

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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},
}

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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

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License

MIT-licensed.