10
votes
Accepted
FFT to spectrum in decibel
Definitely you will have to calibrate your system. You need to know what is the relationship between dBFS (Decibel Full-Scale) and dB scale you want to measure.
In case of digital microphones, you ...
- 10.5k
8
votes
Accepted
STFT: why overlapping the window?
We always want to apply some kind of a window function in order to minimize the effect of leakage. This makes rectangular window (lack of any windowing) case never used, this is why:
Any tapering ...
- 10.5k
8
votes
Accepted
Advantage of STFT over wavelet transform
Wavelet transforms and short-term/short-time Fourier transforms are broad names for classes of transformations that are not totally distinct and may overlap (pun intended).
Both can be efficient for ...
- 29.9k
6
votes
What is first order difference?
The first-order difference operation is a technique for numerical differentiation. It is the simplest method that I know of, and consists of just treating a discrete-time signal as piecewise linear ...
- 23.7k
6
votes
Accepted
STFT amplitude normalization, librosa library
I did answer a similar question a few years back, but can't find it. Basically, you are losing the energy because of the windowing. It's true to say that you should multiply the spectra by 2 in order ...
- 10.5k
5
votes
STFT and DWT (Wavelets)
The short-time Fourier transform is generally a redundant transformation, usually implemented with the same subsampling over every frequency. If the window is well chosen, it is complete: you can ...
- 29.9k
5
votes
FFT to spectrum in decibel
Some details to Jojek's post. Shared here for future reference.
The key is to take the window in consideration and taking a reference ref which corresponds to ...
5
votes
Understanding overlapping in STFT
I understand the concept of the STFT. In order to avoid spectral leakage, you use a hann window that overlaps by 50%.
I'm sorry but you have a misunderstanding of spectral leakage in addition to how ...
- 26.7k
5
votes
Signal processing techniques for an accelerometer signal?
I'm wondering why the STFT pops out. To me, wouldn't a simple threshold on the signal itself or on its envelope do better / just as well, after removal of the g ...
- 22.3k
5
votes
Signal processing techniques for an accelerometer signal?
If this graphics represents the most typical application scenario, then I would go for some simple short window variance estimation and perform thresholding afterwards;
$$ \sigma_x^2 = \frac{1}{N} \...
- 26.7k
5
votes
Window period(overlap) and FFT
In addition to what others have already said, I'll try to answer it from a purely practical point of view (this is also a variant of the overlap-add technique).
If your FFT length is 2048, then an ...
- 881
4
votes
Illustration of time domain aliasing cancellation (TDAC, MDCT, lapped transform)
Edit: I have recently created two Jupyter Notebooks that illustrate this behaviour and let you play around with some actual matrices and actual signals.
I find understanding MDCT easiest if we define ...
- 417
4
votes
Why is the name "Phase vocoder"?
The short-time Fourier transform (STFT) refers to the time-frequency representation of a signal, which is given by:
$$X(\tau,\omega) = \int_{-\infty}^{\infty}x(t)w(t-\tau)e^{-j\omega t} \, dt$$
...
- 194
4
votes
Why is the name "Phase vocoder"?
A vocoder is a type of synthesizer originally developed for speech (or the human voice, thus the "vo" prefix), even before the use of digital processors. The Bell Labs Voder was demonstrated in 1939, ...
- 33.9k
4
votes
Issue with the time vector returned by $\tt signal.spectrogram$ function
The default parameters of signal.spectrogram are:
nperseg = 256
noverlap = nperseg/8 = 32
This means that:
The length of ...
- 10.5k
4
votes
Welch spectrogram
Reading the documentation for scipy.signal.spectrogram I noticed that it does not do any kind of periodogram averaging. It simply splits up the signal into (...
- 4,014
4
votes
Accepted
How to interpret the effect of different windows in short time fourier transform?
A widnow $w[n]$ truncates and weights (tapers) an input signal $x[n]$, to produce $v[n] = x[n]. w[n]$., for subsequent spectral analysis of $x[n]$. A windows's effect on the input signal's true ...
- 26.7k
4
votes
Accepted
Is "Windowed Fourier Transform" a synonym for "STFT"?
In Chapter 2.4 Previous Work of The Short Time Fourier Transform and Local Signals, S. Okamura, 2011, one reads:
The STFT is also known under many names such as the windowed Fourier
Transform, ...
- 29.9k
4
votes
Accepted
Is it possible to recover a waveform from spectrograms of magnitude *and* phase?
Real/imaginary or modulus/phase are two representations of a complex number that carry the same level of information. Then, a STFT is a redundant mapping from a space of functions over a 1D variable (...
- 29.9k
4
votes
Does it make sense to use a wavelet that is equal to a sine of one period?
With all due caution, no in both cases (title and body question). I'll start with the second one.
Continuous wavelets use all dilations of the mother wavelet, which are not accessed with the STFT
...
- 29.9k
4
votes
Advantage of STFT over wavelet transform
STFT is frequency-shift equivariant - same absolute shift has same effect on representation regardless of original frequency${}^1$:
$$
\hat x(\omega) \rightarrow \hat x(\omega - c) \Leftrightarrow \...
- 5,005
3
votes
Accepted
STFT Window Size is 2048, Why is the output 1025?
The continuous Fourier transform possesses symmetries when computed on real signals (Hermitian symmetry). The discrete version, an FFT (of even length) possesses a slighty twisted symmetry.
The DC ...
- 29.9k
3
votes
Accepted
Approximation of Hilbert Transform Using Very Short Hilbert Transform FIR / IIR Filter
This is more like an extended comment to chart the possible answers.
Hilbert transform is a frequency domain 90-degree phase shift of the signal. It has an antisymmetrical impulse response around ...
- 12.4k
3
votes
Accepted
Could not construct original matrix using SVD
Don't have enough reputation to comment but you need to use the conjugate transpose in your formula for the result to be correct. So try stftb=U*S*V'; in the last ...
- 195
3
votes
Choosing the right overlap for a window function
I tried my best but I couldn't find a resource that would list the "good" overlap factors for common and less common windows.
Here's a list of window functions and overlap factors that have constant ...
- 15k
3
votes
Accepted
Meaning of Hop-Size in Filter Bank Interpretation of Short Term Fourier Transform
Your message was apparently unfinished ('When reading about the DCT...'). I thus will be starting from it.
The JPEG compression format is an example of hopping. A DCT-filter bank (Discrete Cosine ...
- 29.9k
3
votes
What do I lose when I set overlap rate to a really high value in STFT
If you don’t care about computational costs, you can start a window at each sample (e.g. 100% - 1 sample overlap). It’s well into diminishing returns, but phase vocoder estimation methods work ...
- 33.9k
3
votes
Accepted
Inverse Fast Fourier with overlap
There are several ways.
Start with taking the iFFT of $ S^{(1)} $ and $ S^{(2)} $. Let's call the results $ m^{(1)} $ and $ m^{(2)} $, since they are modified. They are back in the time domain and ...
- 6,895
3
votes
Accepted
How to calculate the PSD from the complex calculated STFT?
In general, if you have complex spectrum and need PSD in dB the mathematical equation is
$$P_{xx} = 20\cdot\log_{10}|X_{x}|,$$
where $P_{xx}$ is your PSD in dB and $X_{x}$ is your complex STFT ...
- 76
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