Questions tagged [time-frequency]
The time-frequency tag has no usage guidance.
273
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jumps in spectrogram of frequency ramping
I create spectrogram of a sine wave that changes its frequency from 60 MHz to 70 MHz over a period of 1 millisecond.
can someone help me understand why I see those jumps? how can I make it smoother?
<...
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How to extract the oscillation frequency from the following signals?
Signals contain both transient and stabilizing processes.
In the transient process, the signal exhibits oscillatory behavior with damping. Is there some efficient algorithms to extract the frequency? ...
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Anonymize / Obfuscate speech when doing audio classification
Let me preface that I am new to audio processing and audio analysis ;) (I asked the same question on reddit, I wanted to increase it's reach))
I am trying to classify specific events (like a gong or ...
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How to find median position of a contour that represents a peak?
I was reading some papers on time-frequency methods of signal analysis and I am confused about one concept. The idea in these works is to plot a power spectrum in time-frequency plane and then to ...
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The uncertainty principle - Why does it imply that we can't localise
The uncertainty principle states that if you have a signal which is very concentrated in time, then its Fourier transform will be rather outspread and vice versa. However, I don't really understand ...
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STFT needs circular shift or not?
In some textbooks and websites, circular shift operation is done before doing FFT of windowed data, in the explaination, circular shift is to ensure zero-phase. But in other textbooks and websites(I ...
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243
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Increasing STFT resolution by repeating the window? Ways to improve STFT resolution?
In theory of FT(Fourier transform) and STFT(Short Time Fourier Transform) it is said that "A narrower window gives good ...
- 135
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Wavelet signal analysis approach for multi-mode, noisy signal
I have a signal that I am trying to analyze via Matlab's CWT functions. The signal has two distinct oscillating components and I would like to extract the decay factor from each of them. Here is what ...
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How would I figure out the frequency with which a recording of vibrato oscillates? [duplicate]
I'm not sure what the correct signal processing tool for this task is. My file is in m4a format. I'm comfortable using Python (arbitrary library(ies)) or MATLAB, but don't need code, just advice on an ...
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Ambiguity function volume
I find myself confused how two properties of the ambiguity function relate to one another.
The properties in question are (presented here from wikipedia, but similar formulas can be found in books by ...
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Inverse of wavelet transform modulus gives poor results
I just want to understand, why is the result of my wavelet(?) transform so bad.
For $0\le i< k$, where I set $k$ to $10$, I split the signal in blocks of length $s_i:=2^{i+2}$, overlapping by $s/2$...
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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 ...
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168
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What do computed CWT frequencies and color values correspond to?
I wanted to make wavelet transform and represent the frequencies as function of time instead of the scale of the wavelet as function of time. This example that uses ...
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Can finite Multi-Resolution Analysis satisfy the Littlewood-Paley Criterion (unity partition)?
Suppose we are working with a multi resolution analysis (MRA) of $L^2(\mathbb{R})$ and let $\phi$ be the corresponding scaling function and $\psi$ the derived wavelets. Using standard notation with $\...
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A mathematical justification of discontinuity detection using STFT
I'm trying to detect rapid changes in a one-dimensional signal say $[0,1]\ni t \mapsto f(t) \in [-1,1]$. By rapid changes, I mean corner points, edges, or sharp transitions at a point for example the ...
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Littlewood-Paley Conditions, Scattering, and Multi-Resolution Analysis
So I am trying to understand the scattering transform on graphs (GST). There are many formulations but I am stuck on equation 8 in this paper. Here they give a condition on a wavelets that looks like ...
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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 ...
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Does overlapping windows while processing a signal produce a stretched time domain?
I'm very new to signal processing and attempting to implement a spectrogram generator to learn more about DSP in general. So far, I have built up an understanding of how I might do that.
Get input ...
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Inverse continuous wavelet transform, how to obtain fluctuations at a given scale with ssqueezepy?
How can I obtain the fluctuations of a timeseries at a specific scale using the ssqueezepy library for inverse continuous wavelet transform (ICWT)?
I have a minimum reproducible example that uses the ...
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336
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Inverse continuous wavelet transform off by constant factor in the y axis
I have implemented the Continuous Wavelet Transform using the pycwt library(https://github.com/regeirk/pycwt/blob/master/pycwt/wavelet.py) and its inverse using Morlet wavelets, however, upon ...
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Comparison of WVD vs STFT Spectral analysis in the presence of Noise
This question is an extension to the question about WVD vs STFT originally posted Here. During the QA it was pointed out that the WVD only works for noiseless signals.
To test that out I created a ...
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Demonstrating zero phase of vertically symmetrical signals
I'd like to get a zero phase for vertically symmetrical signal (as it done here, FIGURE 10-7).
For this purpose, I tried to test it on gaussian signal in Python:
...
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134
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Bode Plot - Why we add dB value in some situations?
Question: Specify the straight -line approximation of the Bode magnitude plot: $$H(j\omega) = 0.04 \cdot \frac{jw+50}{jw+0.2}$$
I don't understand that in the plotting part we add 6dB for two ...
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672
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Wigner-Ville Distribution (WVD) vs STFT for Spectral Analysis
What are the Pros and Cons of using Wigner-Ville Distribution for spectral analysis of a signal vs taking the STFT. When is it appropriate to use one over the other and is WVD used in real-time ...
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151
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How does slow-time FFT detect velocity?
The signal processing steps for a pulsed radar are: Fast time matched filter -> Slow time FFT.
I cannot understand how is the second step able to detect frequency,
because the results after the ...
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549
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Power/Energy from Continuous Wavelet Transform
How can power or energy be computed from Continuous Wavelet Transform? Is it just $\sum |\text{CWT}(x)|^2$, or are there other considerations, particularly if interested in a subset of frequencies?
Do ...
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How to validate a wavelet filterbank (CWT)?
I've seen many different implementations of CWT, especially in generating the wavelets. Often these implementations produce significantly different outputs - e.g. ...
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Do the first k elements of DFT (Xn) correspond to k lowest frequency components?
Do the result of DFT (Discrete Fourier Transform) of a 1D sequence order as low frequency to high frequency? and why is that?
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842
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Order of using FFT, IFFT, FFT shift and IFFT shift
I considered a time sequence of sine wave t = [0,0.707,1,0.707,0,-0.707,-1,-0.707]
I took spectrum = fft(t) and got the ...
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Understanding negative power in a time frequency heat plot
I am into analyzing EEG signals with the help of this guide. So, I choose to inspect power in a frequency region before and after an event of interest (at t=o) and ...
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Why does a signal with constant frequency have spots that changes colors at a specific value of scale (and so frequency) in the scalogram?
I am studying the Wavelet transform and I am considering this example that I took from PyWavelets documentation. The signal in time domain has the following shape:
Till the value of zero on the ...
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Time Frequency Analysis Equation Derivation
I have been reading Leon Cohen's book "Time Frequency Analysis" as part of a project for university. On page twelve or equation (1.57) during his derivation of a representation of the ...
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109
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Instantaneous frequency vs time for a piecewise signal
I sample a signal that consists of a train of pulses which are amplitude and frequency modulated. I would like to generate a plot that is instantaneous frequency vs time. I compute the Hilbert ...
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Resampling a signal with variable frequency [duplicate]
I haven't touched my signal processing courses for a long time and I forget how to work with these kinds of signals.
I have a signal that comes from a sensor that has 3 time periods.
The time vector ...
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449
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Choice of relationship between n_fft and window_length in STFT
Not a veteran in Signal Processing, it would be extremely appreciated to help me understand the idea/heuristic behinde the idea in STFT that
$$\text{nfft} \ge \text{window length}$$
At least from a ...
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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 ...
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How can I correctly illustrate the impact of a Fractional Fourier Transform on a signal's Wigner-Ville Distribution?
A linear frequency modulated chirp signal produces a Spectrogram and Wigner-Ville Distribution that look like this:
My understanding of the fractional Fourier transform is that it corresponds to a ...
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109
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Random telegraphic noise and Lorentzian noise power spectral density
Following the example of the Lorentzian noise power spectral density shown above (ref), I would like to clarify the following:
In the first figure (labeled by (c)), May I please know why the constant ...
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242
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"Instantaneous impulse response" in a linear time-varying system
I have a LTV (linear and time-varying) system. So, $h(\tau, t)$ is the "instantaneous impulse response" at time $t$ such that if the input signal is $x(t) = \delta(t - t_0)$ (an impulse at ...
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Scaling factor in DFT: pure math or bandwidth issues?
I'm trying to match the amplitudes of a signal before performing DFT and after. So, let's consider a 64-point sine signal with amplitude of $1$:
The DFT of such a signal will give us the amplitude (...
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80
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Value of getting frequency bands of FFT for EEG signals
I'm trying to analyze and extract some frequency domain features for a simple machine learning model from EEG signals.
I partitioned my data to 30s epochs and used np.fft to get the frequency and the (...
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336
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Interpretation of wavelet trasformation (synchrosqueezing)
I'm working on a dataset of spectroscopies and i'm classifying them by transforming the 1D signal into a 2D one by the ssqueezepy library.
For instance, consider to ...
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Energy in frequency and time domain
I know from Parseval's Theorem that, given a signal $x(t)$, with $t$ a variable in the time domain,
$$
\int_{-\infty}^{+\infty} |x(t)|^2 dt = \int_{-\infty}^{+\infty}|X(f)|^2 df,
$$
where $|X(f)|$ is ...
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Why is automatic modulation classification hard?
There is a huge amount of research into automatic modulation classification (AMC) using machine learning.. Why is AMC a hard/difficult problem that we need to use machine learning or even deep ...
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Is online Continuous Wavelet Transform possible?
I have recently created a real-time STFT with 50% overlap.
I wanted to know if this window-based is possible for scalogram, especially continuous wavelet transform. I haven't found anyone ...
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499
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FFT with High Time and Frequency Resolution
Can anyone describe in a bit more detail or provide references to the techniques for simultaneous enhancements to time and frequency resolution described in a high level in HEAD acoustics ...
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Why does using a log scale ruin (warp) my scaleograms?
I'm trying to make a scaleogram of neural data using the continuous wavelet transform (with Morlet wavelets). As a starting point, I use just a simple sine wave built from two frequencies, 50 and 80 ...
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How do I solve for the normalization constant of a discrete time-frequency Gabor atom?
Given the mathematical expression for the discrete Gabor time-frequency atom
$$g_{s,u,\omega,\theta}(n) = \frac{K_{s,u,\omega,\theta}}{\sqrt{s}} e^{-\pi(n-u)^2/s^2} \cos[2\pi\omega(n-u)+\theta]$$
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How to interpret ADEV plot?
I want to understand how to interpret ADEV plots. I was of the understanding that if we see a peak at 1sec of TDEV plot there is a 1Hz noise in Time Interval Error(TIE) Capture.
To understand the ...
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A case that zero padding increase real resolution and extract more info than naive DFT?
It is widely accepted that zero padding cannot reconstruct more information that is originally present in the sample data, which I think is intuitive, because zero padding adds no more information.
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