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Questions tagged [stft]

Short-Time Fourier Transform

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22 votes
2 answers
11k views

Inverse Short Time Fourier Transform algorithm described in words

I'm trying to conceptually understand what is happening when the forward and inverse Short Time Fourier Transforms (STFT) are applied to a discrete time-domain signal. I've found the classic paper by ...
Nicholas Kinar's user avatar
19 votes
5 answers
21k views

How do I optimize the window lengths in STFT?

I have many EEG signals and I want to analyze them using linear methods such as STFT (Short Time Fourier Transform). In STFT , How can I optimize the analysis window length, to reflect the frequency ...
Maen's user avatar
  • 191
14 votes
1 answer
16k views

Comparison between Fourier transform, short-time Fourier transform and wavelets

What is the difference between the Fourier transform, short-time Fourier transform and wavelets?
student's user avatar
  • 141
14 votes
4 answers
17k views

Can you increase frequency resolution of FFT without increasing window size?

I'd like to use STFT for multipitch analysis. I realise detecting the partials existing in the signal is just the beginning. Still I have problem with it. Let's say I have signal sampled with 'CD' ...
nuoritoveri's user avatar
14 votes
3 answers
5k views

STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With ...
Basj's user avatar
  • 1,277
11 votes
2 answers
4k views

Real-Time Human Pitch Detection

I'm trying to implement a singing game that will analise raw mic input and tell the player how good is he singing. That needs to be done in real-time. I've come across a lot of threads asking the ...
Felipe Lira's user avatar
11 votes
3 answers
18k views

STFT: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
kuku's user avatar
  • 273
11 votes
4 answers
5k views

What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
endolith's user avatar
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9 votes
1 answer
3k views

What is the maximal frequency resolution for Matlab's STFT implementation spectrogram()?

Matlab's spectrogram() function calculates the STFT of a signal. It describes its NFFT argument as follows: ...
Andreas's user avatar
  • 1,968
8 votes
4 answers
3k views

Advantage of STFT over wavelet transform

I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion. So, I wonder if there is any advantage of using STFT than WT, and if so, what are ...
lemoncake's user avatar
  • 103
8 votes
2 answers
2k views

Signal processing techniques for an accelerometer signal?

I am running some tests where I am recording accelerometer measurements. I am looking to use elements of signal processing on this signal, but I am unsure about where to begin, or what my approach ...
Gary's user avatar
  • 345
8 votes
2 answers
2k views

Time resolution of the Short Time Fourier Transform (STFT)

I'm struggling to figure out how the time points of an STFT are calculated, and I can't find a definitive answer. Let's say I have a 4Hz stationary signal and I'm going to use a 64 second window with ...
Alex Shaykevich's user avatar
8 votes
3 answers
439 views

How critical is the selection of the window function in STFTs?

I have a sum of periodic signals that I am trying to untangle using time-frequency analysis. I seem to get wildly different results depending on the window length and shape. This is a problem because ...
Emre's user avatar
  • 2,877
8 votes
5 answers
12k views

What is really the Mel-filterbank?

After applying STFT to a signal, you typically need to convert the frequencies to the Mel scale. Typically the frequency values range from $0$ to $N/2$, where $N$ is the width of each sliding window. ...
Francesco Ladogana's user avatar
8 votes
1 answer
1k views

Least Squares Re Synthesis of Short Time Fourier Transform (STFT)

Working with my own MATLAB implementation of the short-time Fourier transform (STFT), I've managed to write code for the analysis step where a 1D time-domain signal $s[t]$ is progressively windowed, ...
Nicholas Kinar's user avatar
7 votes
2 answers
7k views

Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
Avinash Baldi's user avatar
6 votes
4 answers
18k views

Choosing the right overlap for a window function

On Wikipedia there is quite a list of window functions. However, when you are doing a lot of STFTs, you often have to have some overlap to get better results. Generally an overlap factor of 2 (i.e., ...
Jean-Michaël Celerier's user avatar
6 votes
1 answer
645 views

Equivalence between "windowed Fourier transform" and STFT as convolutions/filtering

I've heard, that "windowed Fourier transform" is but one perspective on STFT, and that STFT is fundamentally convolutions of windowed complex sinusoids with the input, i.e. bandpass ...
OverLordGoldDragon's user avatar
6 votes
3 answers
1k views

Role of window length and overlap in uncertainty principle?

I am trying to predict epilepsy using spectrograms and a convolutional neural network. So far I have achieved a validation accuracy of 86% which i feel like is pretty good. Lots of the papers doing ...
niklas Munkholm Hjort's user avatar
6 votes
1 answer
6k views

STFT amplitude normalization, librosa library

So librosa.core.stft returns a complex single sided spectrogram. My question is: What normalization of the amplitude values should I perform afterwards? I believe I have to multiply the amplitude ...
sdiabr's user avatar
  • 209
6 votes
3 answers
383 views

In the formula for the windowed Fourier transform, why is the complex-exponential term not time-shifted to the position of the window?

I have a question about the "windowed / short-time / short-term" Fourier transform that is somewhat perplexing me. I have now added an Addendum at the bottom, where the issue is presented more ...
Julian Newman's user avatar
5 votes
4 answers
799 views

Why are there beats in spectrogram / Windowed Fourier Transform of sines?

I am trying to understand how the Windowed Fourier transform works, so I used Matlab to create an artificial signal, and plotted the Windowed Fourier transform using a gaussian window. $x(t) = \left\...
meta_warrior's user avatar
5 votes
4 answers
57k views

FFT to spectrum in decibel

Here is a 10 seconds-long 440hz sine wave normalized at $0\textrm{ dBFS}$. When computing the STFT (with the code below) of this audio file, I noticed that ...
Basj's user avatar
  • 1,277
5 votes
3 answers
1k views

Is "Windowed Fourier Transform" a synonym for "STFT"?

Sometimes I find the notation WFT (Windowed Fourier Transform) while other times I see STFT (Short Time Fourier Transform). Are they the same?
Diego Sacconi's user avatar
5 votes
2 answers
4k views

Meaning of Hop-Size in Filter Bank Interpretation of Short Term Fourier Transform

The Short Term Fourier Transform (STFT) is used to obtain the time-varying spectrum from a signal. There are two ways to understand it - the overlap add interpretation, and the filter bank ...
Samyukta Ramnath's user avatar
5 votes
1 answer
5k views

STFT Window Size is 2048, Why is the output 1025?

I feel like I am having a brainfart over here and can't seem to remember what's going on with STFT outputs. Consider these two lines of code from the Python library Librosa: ...
syyc8A3QierDK4G's user avatar
5 votes
1 answer
828 views

How to reduce synthesis artifacts produced by phase vocoder?

I implemented the phase vocoder algorithm in Python to time-stretch speech signals by following this paper and referring to this MATLAB tutorial. I can distinguish words in the original signal from ...
Steven Chan's user avatar
5 votes
1 answer
120 views

Interpolation of STFT between time and frequency bins

I am trying to identify and remove airplanes in a time series obtained at a radio meteor receiver. Here we have a spectrogram which displays the power content of my signal as a function of frequency ...
Vakeras's user avatar
  • 51
4 votes
2 answers
962 views

How does the effect of windowing change with the phase of the input signal?

I am calculating the SNR (signal power to noise power) for a sine wave. I don't have an integer number of periods in the waveform being analyzed, so I am using a flattop window to reduce spectral ...
DavidG25's user avatar
  • 119
4 votes
3 answers
11k views

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%. However, the problem that I have, is that the example code online does not account ...
John Menoso's user avatar
4 votes
1 answer
6k views

What is first order difference?

I don't understand what is a first order sequence. For more context: I am reading a paper where the author extracts different sequences (in the STFT domain) and then "The resulting sequences are ...
KM158's user avatar
  • 41
4 votes
3 answers
17k views

Window period(overlap) and FFT

How does changing the window period (i.e the number of points overlap between two frames) affect the FFT results ? Suppose that a time series signal was converted to frequency domain by FFT with ...
Kanmani's user avatar
  • 151
4 votes
3 answers
5k views

Filtering with STFT

I have sucessfully implemented a STFT (+inverseSTFT with perfect reconstruction of original signal, with overlap add, etc.) in order to work on audio files. Using this STFT / iSTFT framework, I have ...
Basj's user avatar
  • 1,277
4 votes
2 answers
1k views

STFT calculation with Gaussian Window

$$ f(t)=\exp(jat^2) \,\,\, and \,\,\, g(t)\,\,is\,\, a\,\, Gaussian\,\, Window:$$ $$ g(t)= \left (πσ^2\right)^{\frac{-1}{4}}\exp\left (\frac{-t^2}{2σ^2} \right ) , \,\,\,\,\,\,\left \|g(t) \right \|=...
MJ13's user avatar
  • 285
4 votes
1 answer
3k views

Is it possible to recover a waveform from spectrograms of magnitude *and* phase?

It is my rough understanding that a typical spectrogram discards phase information by squaring only the real-valued part (magnitude) of the STFT (I know it's not quite this simple, but feel free to ...
lnNoam's user avatar
  • 143
4 votes
3 answers
4k views

What is the relation between windowing and hopping in audio DSP

While using short-time Fourier transform (STFT), it is common to use window function, usually tapered. Will this not alter the original signal $x[n]$ and the STFT may no more be the true STFT of $x[...
Aravinda Murthy's user avatar
4 votes
2 answers
896 views

How to calculate short-time fourier transform (STFT) when the window length is greater or smaller than the FFT size?

I have been trying to understand the weighted overlap-add (WOLA) method. By searching papers and posts in dsp.SE, I found that the window length can be larger and smaller than the FFT size. 1. Window ...
ecook's user avatar
  • 379
4 votes
1 answer
655 views

Detecting background noise from audio time-freq domain analysis

I have a requirement to detect/reduce sidetalk/background noise in real-time audio. I am stuck in how can I detect this from audio time-frequency domain analysis. I am already getting the time-freq ...
Nafiul Alam Fuji's user avatar
3 votes
5 answers
2k views

How to interpret the effect of different windows in short time fourier transform?

There are many categories of windows, e.g., rectangular, Gaussian, and triangular. What are their effects on STFT?
ZHUANG's user avatar
  • 169
3 votes
4 answers
3k views

How to derive the bin width / maximum frequency of DFT/STFT

The bin width is given by the $F_s / N$ and the maximum frequency is given by $F_s / 2$ where $F_s$ is the sample rate and $N$ is the number of samples of the DFT. Going between these is trivial, but ...
Tom Huntington's user avatar
3 votes
2 answers
358 views

What is the cause of STFT artifacts when different signals overlap?

I'm trying to learn about why signals that cross in an STFT cause apparent artifacts in the magnitude. I've been looking at the example below, written in python, where a gaussian peak overlaps with a ...
mgpanas's user avatar
  • 31
3 votes
1 answer
4k views

Confusion with regards to STFT and MFCCs

I'm wondering if someone can clear the following up for me as I'm having a difficult time understanding the concept. I'm looking to implement and learn about the processes and uses using short-time ...
Phorce's user avatar
  • 485
3 votes
3 answers
400 views

Does it make sense to use a wavelet that is equal to a sine of one period?

Would I get same results with STFT method (short-time Fourier transform) if I try this?
John's user avatar
  • 31
3 votes
2 answers
1k views

Amplitude extraction using STFT

I'm trying to recover amplitude/magnitude from an audio stream. I'm using FFT to go from time domain to frequency. If I feed in a signal of known amplitude, the results I get from either windowing or ...
dizzy's user avatar
  • 253
3 votes
1 answer
3k views

length of window and overlap rate in STFT

I want to use STFT to analyze my signal and am wondering what are differences between two solutions: Use short windows (for ex. 256 samples window) Use longer windows (to get higher resolution in ...
Mai's user avatar
  • 329
3 votes
2 answers
428 views

Why does Matlab spectrogram look stripy when windowed input is zero-padded?

I am working on a little project, and stumpled upon something I cannot understand yet. I am learning cognitive science, and don't have DSP knowledge background, only learning from what I find on the ...
LimeAndConconut's user avatar
3 votes
3 answers
3k views

Difference between librosa.stft and scipy.signal.stft

I read the source code of librosa.stft and sicpy.signal.stft, and notice that the calculation results of STFT in these two libraries are quite different: In scipy.signal.stft, the stft result is ...
Xiong's user avatar
  • 41
3 votes
1 answer
2k views

Illustration of time domain aliasing cancellation (TDAC, MDCT, lapped transform)

Can someone find or make a visual illustration of how time domain aliasing cancellation works in lapped transforms such as the MDCT? I think a graphic would make it a lot easier to understand, and I ...
endolith's user avatar
  • 15.8k
3 votes
2 answers
370 views

Optimize window length (STFT) via gradient descent (in neural networks)

The authors from this paper optimized a Gaussian window size via gradient descent (the σ parameter of the bell curve) together with the other parameters of neural networks. I don't use Gaussian window ...
JXuan's user avatar
  • 55
3 votes
1 answer
1k views

Approximation of Hilbert Transform Using Very Short Hilbert Transform FIR / IIR Filter

Hilbert transform is a quite sensitive topic here, since Gabor's paper, Theory of Communication, J. Inst. Electr. Engineering, London, 1946. Perhaps even more important than the Fourier transform. ...
Laurent Duval's user avatar

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