Questions tagged [time-frequency]

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0 votes
1 answer
39 views

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 ...
0 votes
0 answers
33 views

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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1 vote
0 answers
23 views

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 ...
2 votes
1 answer
51 views

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 ...
3 votes
2 answers
233 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 ...
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0 answers
68 views

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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2 votes
0 answers
34 views

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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3 votes
1 answer
91 views

"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 ...
  • 301
0 votes
1 answer
51 views

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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0 votes
0 answers
29 views

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 (...
2 votes
2 answers
147 views

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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0 votes
0 answers
40 views

A python-based implementation of time-frequency block thresholding for audio signals?

I'm looking for a python implementation of the block-thresholding algorithm introduced in this classic paper. I've been searching a while but I couldn't find it :(. There is of course a Matlab ...
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1 vote
1 answer
70 views

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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1 vote
2 answers
41 views

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 ...
  • 135
0 votes
1 answer
87 views

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 ...
5 votes
4 answers
176 views

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 this video? Can anyone ...
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-1 votes
1 answer
103 views

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 ...
1 vote
1 answer
38 views

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 $$g_{s,u,\omega,\theta}(n) = \frac{K_{s,u,\omega,\theta}}{\sqrt{s}} e^{-\pi(n-u)^2/s^2} \cos[2\pi\omega(n-u)+\theta]$$ ...
0 votes
1 answer
144 views

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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5 votes
3 answers
814 views

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. ...
0 votes
1 answer
399 views

How to set the "widths" parameter for continuous wavelet transform using Morlet wavelets? (scipy.signal.cwt)

I'm trying to use scipy.signal.cwt() to do a time-frequency decomposition of neural data. However, I don't completely understand the "widths" parameter. I ...
1 vote
0 answers
45 views

How to restore time domain signal after multiply cosine signal when cosine signal has unknown initial phase?

I use AD9954 as cosine signal generator,then use ad835 to multiply this cosine signal with antenna signal. As ,the antenna signal frequency shifted after ad835,then ...
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2 votes
1 answer
102 views

difference in the spectral densities of autoregressive sequence by FFT and analytical solution

I want to obtain the power spectral density (PSD) of an autoregressive sequence, AR(1). The analytical solution according to this reference (page 12) is For $X_t = \phi_1X_{t-1}+W_t, W_t \sim N(0,\...
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1 vote
3 answers
111 views

Is digital necessarily discrete in both amplitude and time?

Is digital necessarily discrete in both amplitude and time? Or rather it is necessarily discrete only in time (but not necessarily in amplitude)?
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3 votes
1 answer
170 views

Why signal add noise cause signal undiscoverable after `fft` and `ifft`?

As we all know, Fourier transform of the sinc(t) is rect(f). Simple python script to discover signal after fft and ifft with ...
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2 votes
4 answers
331 views

Methods to increase FFT time resolution without lowering FFT size

It is known that in FFT time and frequency resolution are inversely related if FFT resolution is increased then time resolution will decrease. However is it possible to overcome issues in time ...
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1 vote
1 answer
202 views

How to make a time/period (1/frequency) plot with CWT

This is a question about producing a time/period (1/frequency) plot from a CWT, instead of the time/scale output. I am trying to use the ssqueezepy python library to perform the CWTs. Then I ...
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1 vote
1 answer
34 views

The separation condition of a multi-component signal

Suppose a signal is a superposition of multiple intrinsic-mode-type (IMT) functions, say $$f(t) = \sum_{i=1}^n A_i(t)e^{i\varphi_i(t)} $$ Why is the separation condition of $f(t)$ be $$\forall i,j \...
2 votes
1 answer
169 views

Impulse response of Time Varying Channel

I have just started studying LTV channels in wireless communication. I know that $y(t) = \int _{-\infty} ^\infty x(t-\tau)h(t,\tau)d\tau$ Is there any way we can calculate the Impulse response $h(t,\...
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0 votes
0 answers
50 views

overlap and save method) relation zero padding with double size FIR filter coefficient

i'm doing overlap and save method at frequency domain to do this, i added one block back and forth at filter and signal respectly The problem is my filter is bessel function and that is look like this ...
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2 votes
2 answers
208 views

Misunderstanding of Nyquist sampling theorem and minimum sampling rate

I sample my time-domain (TD) signal using a distance between time-samples of $\delta = (t_{max} - t_{min}) / N_t$, where $N_t$ is the number of samples taken. The sampling rate is $1 / \delta$. I have ...
  • 135
0 votes
1 answer
67 views

Removing Attenuator and Real Mixer influence on the received Baseband signal in Radar IQ Transmitter - De-embedding

Radar IQ Transmitter Measurement Setup: Waveform Generator + IQ Transmitter + Attenuator + Real Downconversion mixer + Oscilloscope + Post-processing (Hilbert Transform) With the above arrangement ...
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0 votes
1 answer
160 views

Joint Time-Frequency Scattering structure & implementation?

How does JTFS differ from wavelet time scattering in its computation graph, and how does FDTS discriminability work, at a lower level? How is it implemented in practice, and how can one visualize ...
1 vote
1 answer
363 views

Joint Time-Frequency Scattering explanation?

How does JTFS work, intuitively? What are its motivations, and how's it differ from the Wavelet (time) Scattering transform? Can it be visualized?
0 votes
1 answer
134 views

Inverting a scalogram

A scalogram is said to discard phase information with modulus; is it still possible to recover the signal to some extent? Algorithms like Griffin-Lim can invert within an error, but what's the ...
5 votes
1 answer
849 views

Wavelet Scattering properties & implementation?

What are the properties of the scattering transform, besides shift invariance and warp stability? How is it implemented in practice, and how can one visualize its computational graph?
7 votes
1 answer
2k views

Wavelet Scattering explanation?

How does Wavelet Scattering work, intuitively? What are its motivations, and how's it differ from the (continuous) Wavelet Transform? Can it be visualized?
1 vote
2 answers
94 views

How to objectively measure how "good" a time-frequency representation of music is?

I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal ...
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0 votes
0 answers
96 views

Gabor uncertainty and time-frequency resolution

I have a question about Gabor's uncertainty theorem, and how it relates to time and frequency resolutions. As I understand it, Gabor's uncertainty theorem states that the standard deviations of a ...
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2 votes
2 answers
81 views

Computable Time-Frequency Distribution without Cross-Terms

Context: I have a single receiver that is receiving multiple signals. Each signal has a few strong harmonics, but I don't know the fundamental frequency. I would like to display them on a spectrogram ...
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3 votes
3 answers
714 views

scipy.signal.spectrogram() - how to handle gaps in the timeseries data

Looking at the magnitude of variable stars - the dataset is from here: https://dogwood.physics.mcmaster.ca/Cepheid/URL/MW/BD-10d4669.html The magnitude plot: ...
0 votes
1 answer
589 views

scipy.signal.spectrogram() with noverlap=nperseg-1, what are the possible side-effects?

I'm using a simulated data set which can be downloaded from the link in the fist paragraph on this page (it's an Excel file): https://www.analyticbridge.datasciencecentral.com/forum/topics/challenge-...
0 votes
1 answer
53 views

Time-frequency analysis of a nonlinear system

I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on ...
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1 vote
2 answers
841 views

What is the advantage of overlapping windows while evaluating Spectrogram?

I've seen many documents that refer to calculate spectrogram through overlapping windows but haven't found clear documents on why this is done and how to calculate the number of points that need to be ...
1 vote
1 answer
186 views

How to Frequency Modulate an Audio Signal

I've started to learn about FM and I followed this guide to FM a sine wave. I have managed to do it and here is the result: And the code: ...
2 votes
2 answers
327 views

How does the scale of a wavelet relate to the Fourier frequency (or period) under CWT?

I noticed that there are many ways to relate the scale factor of wavelets to some characteristic frequency, such as the peak frequency, the central instantaneous frequency, and so on(plz see section 2....
0 votes
1 answer
274 views

Extracting different frequency bands (alpha, beta, gamma) from MEG source estimated data

I have a dataset that consists of source estimated data of MEG brain signals. I need to extract the different frequency band features (i.e., alpha, beta, gamma, etc) from them. What steps/procedure ...
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0 votes
1 answer
61 views

Calculating power of brain signals

I have a dataset that contains EEG (or MEG) recordings of brain signals during some cognitive tasks. Each row, shows the source estimates of neurons in a particular region. source estimate contains ...
  • 149
0 votes
0 answers
62 views

filtering large wiggles in signals

I am trying to filter out large wiggles showing in a signal. Those wiggles are happening due to many signal processing layers and a final sine Fourier transform (no phase) Here's the python code i am ...
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0 votes
2 answers
56 views

unsymmetric fft in matlab

This is the FFT of a 4khz sin signal. I wonder why the negative part and positive part of X axis is not symmetrical? ...
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