Questions tagged [time-frequency]

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Time Frequency bin

I am doing research in audio signal processing for DOA estimation. I came across the term Time-Frequency bin. I have gone through several articles but none of them specify a TF bin rather it specifies ...
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1answer
68 views

Calculating phase shift between two sines of equal, unknown, amplitude and frequency

I've got a source signal $s_1(t)$ and a system affecting that, yielding a phase-shifted version $s_2(t)$; \begin{align} \color{blue}{s_1(t)} &= A\sin(t+\phi_1)\\ \color{red}{s_2(t)} &= A\sin(...
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Time resolution converted in frequency uncertainty

I have an instrument with a time resolution of $\delta t = 2x10^{-5}$ s (see the radio telescope described here). I want to measure periodic signals at a frequency of, say 10.001 MHz. The paper ...
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24 views

How to tell, which coefficient corresponds to which frequency while computing wavelet transform?

I am applying wavelet transform on functional Near Infrared Spectroscopy (fNIRS) signal. My aim is to get the info that which coefficient corresponds to which frequency in the signal. Is it possible ...
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1answer
107 views

Scaling a wavelet in continuous wavelet transform

The mexican hat wavelet, obtained from the second derivative of a Gaussian, has a functional form of $$ \frac{2}{\sqrt{3 \sqrt{\pi} \sigma \ }} \left(1-\frac{t^2}{\sigma^2} \right) e^{-t^2/(2\sigma^...
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1answer
170 views

Relationship between wavelet shape and wavelet filters

MATLAB has a library of wavelet functions, showing their "continuous forms" as well as the the decomposition and reconstruction filters. In decimated wavelet transform the filter size remains the ...
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343 views

Plotting a scalogram of a signal's Continuous Wavelet Transform (CWT) in python

So I've been learning about wavelets for a few weeks because I'd like to use them in a research project I'm working on and I've been trying to grasp the general ideas behind them.I've been struggling ...
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24 views

CWT coefficients as features for ML algorithms

I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
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26 views

Time spans in coherence computation

Currently I'm writing my master thesis and I'm having troubles with coherence definition. My question is similar to https://stats.stackexchange.com/questions/92412/clear-steps-to-calculate-coherence-...
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1answer
50 views

Sampling of frequency response

Let's consider any physical quantity depending on the frequency. For example, the impedance of a certain electrical component: $Z(f)$. Now, imagine to measure it in a continuous interval of ...
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32 views

Why my Time-Frequency plot is time reversed?

I'm trying to build my own code implementation for Continuous Wavelet Fourier Transform. But when I compare the time-frequency plot created with my function with time-frequency plot created with the ...
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1answer
705 views

Python tool for time-frequency analysis

I am trying to perform time-frequency analyses using the PyWavelets (pywt) toolkit for python. My ultimate goal is to perform time-frequency analyses for EEG signals but I am starting with something ...
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21 views

Wignerville of market data [closed]

I am trying to get some insight into market data, in this case the stock KO. Here is the chart: If I take the wignerville of ...
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1answer
50 views

Proof that DFT does not require more than N points

I'm trying to show how the discrete Fourier transform (DFT) arises from the equation for the continuous-time Fourier Transform. I've run into an interesting caveat which I can't seem to find an ...
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114 views

MNE-python time frequency analysis

I usually use Brain Vision analyzer for EEG analysis. Recently, I also do MNE-python. I have already done ERP and time-frequency analysis.I'm trying to get time-frequency power from MNE-python now. ...
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135 views

How to find frequency and corresponding time for an audio signal?

I want to read in a sound file and get the frequency at each time interval of the signal. I thought that the best way to approach this is by applying FFT to small chunks of the signal. Because FFT ...
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15 views

Symmetry in Lomb-Scargle transformation

I'm observing weird symmetry and repeating pattern on my unevenly sampled time series data after Lomb-Scargle transformation. I used astropy lomb-scargle. ...
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3answers
317 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?
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1answer
61 views

What does this spectrogram mean?This is spectrogram of a multitone FM signal

! The spectrogram of FM signal has been generated by using Matlab.Now I want to what does these scratch like lined represent, though I have only two frequency components in my message signal(https://i....
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22 views

Derivation of the reassigned STFT magnitude of a complex exponential

I have a complex exponential defined as $x(t)=Ae^{i2\pi f_{0}t}$ and its short time Fourier transform with respect to the analysis window, $g(t)$ is defined as, $$X_{g}(b,f) = \int_\mathbb{R} x(t+b)g(...
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1answer
106 views

Term for integral multiples of fundamental period?

As we know that a signal has fundamental frequency and integral multiples of fundamental frequency are known as harmonics I am curious about the term that will be used for integral multiples of ...
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18 views

Bandpass filtering with passband changing with time

Is it possible to implement some sort of filter which adapts as a function of time? Specifically, say I have a "noiseless" model of some signal which has the same frequency components at the same ...
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1answer
236 views

Filtering and peak finding

I have an observed signal which is the norm of the sum of two 3-vectors: $$ S(t) = || \mathbf{A}(t) + \mathbf{B}(t) || $$ Now, I have full knowledge of the vector $\mathbf{A}(t)$, $$ \mathbf{A}(t) = \...
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93 views

Filtering frequencies in diferent ranges in Python

I would like to filter frequencies: Alpha, Beta and Gamma. These bands have a relation with the task that I want to classify, I am using the Gumpy python tool which has a method to apply Butterworth ...
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0answers
139 views

Power spectral density of a pulse

A little background: I am simulating the response of an antenna to a pulse. The pulse has a wide frequency range, but the antenna only responds to a fairly narrow frequency. I can extract voltage and ...
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2answers
878 views

Fourier Transform with both Time Delay and Frequency Shift

I know that the Fourier transform of a function with time delay can be written as: $$\mathscr{F}\big\{x(t-t_0)\big\}=X(f)e^{-j2\pi f t_0}$$ The Fourier transform of a function with frequency shift ...
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137 views

How to sample a transfer function (angular spectrum) in the frequency domain?

I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given ...
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2answers
764 views

Stability of system with poles inside unit circle - conflict with differential equation

I am trying to understand why a system with a single pole inside the unit circle is stable. For example, take a system with one pole at $z=\frac{1}{2}$. The literature says the system is stable. As a ...
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2answers
289 views

Other time-frequency-plane tiling than STFT, DWT, ConstantQ-Transform: multiresolution STFT?

It is known that a) the STFT gives a rectangular tiling of the time-frequency plane b) the Wavelet transform gives a non-linear tiling (better frequency resolution for low-frequencies, and better ...
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1answer
133 views

Separate two sinusoids with very close frequencies (5 Hz difference) in a 44.1 Khz audio signal, with good time-domain resolution [closed]

Here is an audio signal which is a mix of (WAV file available here): a 2000 Hz sinusoid, beginning at 1.00 sec, without fade-in/fade-out a 2005 Hz sinusoid, beginning at 1.031 sec, with a slow fade-...
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1answer
335 views

Plotting Hilbert Spectrum from Hilbert Huang Transform

Before anyone calls it a repeat post from past posts. I'd like to point out I've read all of those; however, I have questions on making a hard coded version of the hilbert spectrum. I do indeed have ...
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1answer
527 views

About phase unwrapping

I am not too familiar with phase-related problems so I need some suggestions or corrections in a problem that might be an old but easy one. Here is my problem: given a complex signal: $$y(t) = e^{j\...
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2answers
1k views

Finite and Infinite support in time and frequency domain

It's known that signals with a finite support in time has an infinite support in frequency (talking about Fourier Transforms). A common example that is given for the claim is the triangle function ...
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931 views

How does the Scipy implementation of CWT actually work?

I'm trying to use the SciPy implementation of the Continuous Wavelet Transform to analyze EEG data. I am using The problem is that I have no idea what the width parameter should be. It says that it's ...
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1answer
510 views

Instantaneous Frequency Estimation by Hilbert Transform - Theoretical Justification and Proof

I would like to better understand why the instantaneous frequency estimation by Hilbert transformation works (and especially why it doesn't work / lead to precise results in many cases). The ...
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0answers
92 views

Does anyone recognize this modulation?

I'm trying to extract the code of my garage remote, but i have some difficulty to find witch modulation has been used. At first I thought it was a simple digital modulation, but there is some strange ...
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1answer
120 views

Some doubts in the matlab code of computing Wigner distribution

I found that a discrete form of the Wigner distribution was $$WD(n,k) = \sum_{m = -N/2}^{N/2}f(n+m)f^*(n-m)e^{-j\frac{2\pi}{N+1}2mk}$$ where $f(n)$ is the signal and time limited within $|n|\le N/2$. ...
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0answers
181 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}^{\...
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70 views

Selection of transforms, windows, wavelets for current signal analysis

I am new to this topic but I already read about the propperties of different signal analysis methods. I am stuck with the obvious advantages of FFT, STFT and Wavelet transforms but can't find good ...
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1answer
57 views

Is there a name for the procedure of taking the FT over separate consecutive small time-blocks?

Suppose we have a continuous time-interval $I=[a,b]$, and a signal $x \colon I \to \mathbb{R}$. A procedure that is sometimes carried out (e.g. when doing bispectral analysis) is to partition $I$ ...
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1answer
87 views

Basic sampling excercise - unsure of rationale informing np.arange parameters for time array

I'm extremely new to DSP, so I apologise if it's a very basic question. I'm having issues understanding the following exercise: "Create an array of 201 samples containing a sin wave with a frequency ...
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2answers
466 views

Compensation for Irregular Time Step for DFT (FFT)

I want to run a clustering algorithm (svm, knn) on the ferquency spectrum data of a temperature sensor that published at irregular times. Here is the temperature data to take the FFT: I got the ...
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1answer
5k views

scipy.signal.spectrogram

I want to do time-frequency analysis of a signal. So i decided to use spectrogram function from scipy. This function returns, three parameters f,t,Sxx. I am using below arguements: x : my signal fs : ...
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0answers
101 views

How to derivate in the frequency domain

I have two Time Domain functions, $f_1(t)$ and $f_2(t)$. I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
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2answers
196 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 ...
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1answer
1k views

Fourier transform of function division in time domain

$F_1(\omega)$ is the Fourier Transform of $f_1(t)$. $F_2(\omega)$ is the Fourier TRansform of $f_2(t)$. Can I obtain the Fourier Transform ($F_3(\omega)$) of $$ f_3(t) = \frac{f_1(t)}{f_2(t)} $$ ...
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78 views

Interpretation of instaneous time and instaneous frequency in time-frequency plane?

In this paper: Sparse time-frequency representations, Given signal $x(t)$, the time-frequency representation was got by Gabor transform and was denoted by $\chi(t,\omega)=|\chi(t,\omega)|\exp(\mathrm{...
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1answer
201 views

Why are analytic signals so important in Time-frequency analysis?

I am little confused about why we need analytic signals so bad in time-frequency analysis. What might happen if I use non-analytic signals to do time-frequency analysis?
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1answer
83 views

Dimensional analysis in the Morlet wavelet

I'm a complete beginner on signal processing, so please forgive the basicness of this question - but I'm very confused by this. Regarding the Morlet wavelet, Wikipedia says: The wavelet is defined ...
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1answer
315 views

Finite moving average filter

I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....