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https://github.com/overlordgolddragon/stackexchangeanswers

Codes/images for StackExchange answers
https://github.com/overlordgolddragon/stackexchangeanswers

signal-processing stackexchange stackoverflow time-frequency-analysis wavelets

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Codes/images for StackExchange answers

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README 

        
# StackExchange Answers



[![DOI](https://zenodo.org/badge/387701666.svg)](https://zenodo.org/badge/latestdoi/387701666)



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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



```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](https://dsp.stackexchange.com/a/87512/50076), code Q87355

  2. 🡡 Locating non-homogeneous areas in an image - [Q&A](https://dsp.stackexchange.com/a/75636/50076), code included

  3. 🡡 Estimate sine frequency under white noise - [Q&A](https://dsp.stackexchange.com/a/88711/50076), code Q76644

  4. Extract sine phase and amplitude, accurate and noise-robust method - [Q&A](https://dsp.stackexchange.com/a/88833/50076), code Q29509

  5. Nonlinear filtering and inspection of noisy vibration signal - [Q&A](https://dsp.stackexchange.com/a/84095/50076), code included



#### Intuition / "Deep" Explanations



  1. ✯ Physical significance of negative frequencies - [Q&A](https://dsp.stackexchange.com/a/87994/50076)

  2. ✯ Wavelet "center frequency" explanation, relation to CWT scales - [Q&A](https://dsp.stackexchange.com/a/76371/50076), code Q76329

  3. 🡡 DFT coefficients meaning? - [Q&A](https://dsp.stackexchange.com/a/70395/50076)

  4. 🡡 Why is `|x|^2` power? - [Q&A](https://dsp.stackexchange.com/a/86919/50076)

  5. 🡡 Does zero-padding distort the spectrum? - [Q&A](https://dsp.stackexchange.com/a/70498/50076)

  6. How is a 1D signal considered a "vector"? - [Q&A](https://dsp.stackexchange.com/a/87057/50076)

  7. Are colored images 2D or 3D? - [Q&A](https://dsp.stackexchange.com/a/81831/50076)

  8. Are real-world signals bandlimited? - [Q&A](https://dsp.stackexchange.com/a/75147/50076)

  9. What can be meant by "bandlimited"? - [Q&A](https://dsp.stackexchange.com/a/70949/50076)



#### Measures / Heuristics



  1. ✯ How to validate a wavelet filterbank? - [Q&A](https://dsp.stackexchange.com/a/86069/50076), code to-be-released

  2. 🡡 How to measure aliasing? - [Q&A](https://dsp.stackexchange.com/a/87706/50076), code Q87705



#### Time-Frequency Analysis / Feature Engineering



  1. ✯ Wavelet Scattering explanation - [Q&A](https://dsp.stackexchange.com/a/78513/50076), code Q78512

  2. ✯ Joint Time-Frequency Scattering explanation - [Q&A](https://dsp.stackexchange.com/a/78623/50076), code Q78644

  3. ✯ Synchrosqueezing explanation - [Q&A](https://dsp.stackexchange.com/a/71399/50076)

  4. ✯ Wavelet Scattering properties & implementation - [Q&A](https://dsp.stackexchange.com/a/78515/50076), code Q78512

  5. 🡡 Equivalence between "windowed Fourier transform" and STFT as convolutions/filtering - [Q&A](https://dsp.stackexchange.com/a/86938/50076), code Q86937

  6. 🡡 What is "spin" for the 2D (separable) Morlet? - [Q&A](https://dsp.stackexchange.com/a/86013/50076), code to-be-released

  7. 🡡 Amplitude extraction using STFT - [Q&A](https://dsp.stackexchange.com/a/86731/50076), code Q86726

  8. 🡡 Why are there beats in STFT of sines? - [Q&A](https://dsp.stackexchange.com/a/87086/50076), code Q11333

  9. 🡡 Power/Energy from CWT - [Q&A](https://dsp.stackexchange.com/a/86182/50076), code Q86181

  10. 🡡 CWT vs DWT - [Q&A](https://dsp.stackexchange.com/a/76639/50076) 

  11. 🡡 One-integral inverse CWT - [Q&A](https://dsp.stackexchange.com/a/76239/50076), code included

  12. 🡡 Joint Time-Frequency Scattering structure & implementation - [Q&A](https://dsp.stackexchange.com/a/78625/50076), code Q78644

  13. What do CWT values correspond to? - [Q&A](https://dsp.stackexchange.com/a/86939/50076), code included

  14. Role of window length and overlap in uncertainty principle - [Q&A](https://dsp.stackexchange.com/a/80920/50076), Q80918

  15. Inverting a scalogram - [Q&A](https://dsp.stackexchange.com/a/78531/50076), code Q78530

  16. Importance of overlap in STFT - [Q&A](https://dsp.stackexchange.com/a/76507/50076)

  17. Advantages of complex wavelets over real-valued - [Q&A](https://dsp.stackexchange.com/a/76093/50076)

  18. Bandpass filtering for amplitude - [Q&A](https://dsp.stackexchange.com/a/75819/50076), code included

  19. How is wavelet time & frequency resolution computed? - [Q&A](https://dsp.stackexchange.com/a/72043/50076)

  20. How is wavelet center frequency computed? - [Q&A](https://dsp.stackexchange.com/a/70837/50076)



#### Signal Theory



  1. ✯ DFT of a sine, closed form solution and insights - [Q&A](https://dsp.stackexchange.com/a/88365/50076), code Q87926

  2. 🡡 Subsampling in frequency domain, Effect of sampling rate on spectrum - [Q&A](https://dsp.stackexchange.com/a/87121/50076), code included

  3. 🡡 Why is SNR periodic/sinusoidal for streamed windowing of a sine? - [Q&A](https://dsp.stackexchange.com/a/87933/50076)

  4. 🡡 DFT modulus of a sine, closed form solution and insights - [Q&A](https://dsp.stackexchange.com/a/88400/50076), code Q87926

  5. Relationship between energy, power, and sampling rate - [Q&A](https://dsp.stackexchange.com/a/86132/50076), code Q85745

  6. Hilbert transform for amplitude extraction/demodulation of broadband waveforms - [Q&A](https://dsp.stackexchange.com/a/83257/50076)

  7. Other end of Nyquist limit - [Q&A](https://dsp.stackexchange.com/a/84746/50076)

  8. Instantaneous frequency of a signal - [Q&A](https://dsp.stackexchange.com/a/84144/50076)

  9. DFT filter bank interpretation - [Q&A](https://dsp.stackexchange.com/a/83878/50076)

  10. `ifft` first half of time domain ("DFT unpad property") - [Q&A](https://dsp.stackexchange.com/a/81994/50076), code included

  11. Role of padding in convolution / Alleviating edge effects in Hilbert transform - [Q&A](https://dsp.stackexchange.com/a/76792/50076), code Q76754

  12. How to frequency modulate? - [Q&A](https://dsp.stackexchange.com/a/76482/50076)

  13. Symmetries of analyticity - [Q&A](https://dsp.stackexchange.com/q/76560/50076)

  14. Effect of sampling rate and duration on discrete parameters of sine (spectrum) - [Q&A](https://dsp.stackexchange.com/a/88389/50076)



#### Algorithms



  1. 🡡 2D FFT cross-correlation in Python - [Q&A](https://dsp.stackexchange.com/a/87782/50076), code Q87781

  2. Efficient 2D convolution/cross-correlation along  only one axis (1D output) - [Q&A](https://dsp.stackexchange.com/a/87563/50076), code included

  3. Optimizing window length in STFT via gradient descent - [Q&A](https://dsp.stackexchange.com/a/81627/50076), code Q81624



#### Proofs / Mathy



  1. 🡡 Amplitude extraction / demodulation criteria for Hilbert transform - [Q&A](https://dsp.stackexchange.com/a/83299/50076)

  2. 🡡 Is downsampling LTI for bandlimited inputs? - [Q&A](https://dsp.stackexchange.com/a/88055/50076), code Q88042

  3. 🡡 Sine DFT: N/4-symmetry, bin sinusoidal modulation vs time shifts  - [Q&A](https://dsp.stackexchange.com/a/88421/50076), code Q87926

  4. Inverse CWT derivation - [Q&A](https://dsp.stackexchange.com/a/71148/50076)






### License



MIT-licensed.