Questions tagged [stft]

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22
votes
2answers
10k 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 ...
16
votes
5answers
15k 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 ...
14
votes
1answer
15k 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?
12
votes
4answers
16k 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' ...
12
votes
3answers
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 ...
11
votes
2answers
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 ...
11
votes
4answers
4k 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, ...
10
votes
1answer
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: ...
8
votes
2answers
569 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 ...
8
votes
2answers
1k 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 ...
8
votes
2answers
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 ...
8
votes
3answers
406 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 ...
8
votes
1answer
979 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, ...
6
votes
1answer
14k 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 ...
5
votes
3answers
41k 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 ...
5
votes
4answers
15k 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., ...
5
votes
2answers
3k 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?
5
votes
2answers
299 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 ...
4
votes
3answers
8k 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 ...
4
votes
3answers
130 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 ...
4
votes
2answers
683 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 \|=...
4
votes
1answer
2k 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 ...
4
votes
3answers
3k 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 ...
4
votes
1answer
3k 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: ...
4
votes
1answer
684 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 ...
3
votes
4answers
914 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 ...
3
votes
3answers
361 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?
3
votes
3answers
683 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?
3
votes
1answer
4k 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 ...
3
votes
1answer
5k 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 ...
3
votes
2answers
149 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 ...
3
votes
1answer
1k 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 ...
3
votes
2answers
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 ...
3
votes
1answer
59 views

Given 1 recording of my voice, how can I process it to sound like 2 independent recordings of my voice played in unison?

I have one recording of my voice $x[n]$ singing a song. One thing I could do is independently record me singing the song again to obtain $y[n]$. Then, $z[n] = \frac{1}{2}\left(x[n] + y[n]\right)$ ...
3
votes
1answer
105 views

Frequency estimation on chaotic waveform

The target signal is generated by the following analytically solvable hybrid chaotic oscillator \begin{equation}\label{eq:1} \ddot{u} - 2\beta \dot{u} +(\omega^2+\beta^2)(u-s)=0 \end{equation} ...
3
votes
1answer
315 views

Efficient FFT (or SFFT) for adjacent parts of signal with overlap?

Imaging we have a signal $x$, which is segmented to 50% overlapped vectors $x_1,x_2,..,x_m$ , and we intent to compute FFT of each segment. Is there anyway that we can reduce computation of FFT of ...
3
votes
1answer
6k views

Spectrogram, time vs frequency localization, and length of signal

So I'm having some trouble conceptually and am hoping somebody can clear something up for me. This is long and I apologize for that but I want to provide as much information as possible so that the ...
3
votes
0answers
196 views

Reconstruct signal from its Spectrogram only

The spectrogram of a signal throws away the phase information, but it is said to be possible to reconstruct the signal only from the spectrogram [1] via $$s(t) = \frac{1}{2\pi s^*(0)}\int_{-\infty}^{\...
3
votes
0answers
326 views

Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
3
votes
0answers
259 views

Segment/Idenfication of signal from a spectrogram

I have the following Spectrogram of a signal: Essentially, in this signal, I know there is one point of interest (between 60-80) and between the the particular frequencies. I could, potentially ...
3
votes
0answers
432 views

Why are the frequencies associated with the STFT bins not representative of the energy?

I'm experimenting with a 30 Hz sine wave and I want to extract the frequencies of this, and have implemented the algorithm to do so. This gives a correct reading, well, gives 29 Hz. I'm now wanting ...
2
votes
4answers
1k 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?
2
votes
3answers
706 views

Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)?

First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ...
2
votes
1answer
477 views

How can I find the amplitude of the 20 Hz frequency component of a signal faster?

I have a time varying discrete signal x(t) sampled at 5ms rate. I need to find the amplitude of the 20 Hz frequency component for each sample. What I do today is that for each sample I do a Short-time ...
2
votes
2answers
136 views

What mother wavelet should be chosen as an alternative to the STFT?

The Short Time Fourier Transform (STFT) is used to identify time localized frequency content of a signal. The STFT operates by chunking an input signal into blocks and performing FFT on the block, and ...
2
votes
1answer
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 ...
2
votes
1answer
7k views

Power Spectral Density estimate (PSD)

I'm trying to understand PSD, and, it's functions. So far I have carried out the following: Segmented a signal with NFFT = 256 and ...
2
votes
1answer
51 views

Understanding stability in frame theory. Wavelets

I'm trying to grasp some understanding of the concept of stability in the context of the frame theory. The definition of frame in ref1 states that a sequence of functions $\{ \phi_n \}_{n \in \Gamma}$ ...
2
votes
2answers
1k views

Combining spectrograms with different windows to getting arbitrary time and frequency resolution

Spectrograms convert an amplitude-time signal into a frequency-time signal using Short Time Fourier Transform (STFT). The window size L used in STFT is a design choice. As L increases, you get higher ...
2
votes
1answer
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. ...

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