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Questions tagged [time-frequency]

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367 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 ...
41 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 ...
23 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 ...
4k 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 ...
824 views

Getting frequency content at different times from discrete wavelet transform coeffs

After being away from DSP for a long time, I am trying to familiarize myself with wavelet transform. Here is what I (think) have understood so far: Wavelet transform provides you high time resolution ...
124 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 ...
181 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 ...
271 views

Variance of the Discrete Gabor Transform for practical implementation

When we design a discrete Gabor filter for a 1D signal, how do we determine the variance of the filter, depending on the time step of the signal? Is there any empirical theorem/result that we should ...
39 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 ...
20 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 ...
85 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. ...
59 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 ...
14 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. ...
310 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?
782 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 ...
51 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....
17 views

71 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 ...
88 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 ...
13 views

How to implement freq convolution layer?

I am referring the paper https://pdfs.semanticscholar.org/31c7/4962122ba5fe1c469101b5bc2ae6d88c9c18.pdf. In the paper, for CLDNN network first layer is freq convolution. How to implement the same for ...
237 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 ...
674 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 ...
51 views

How to make function in time domain after fft fit with the corresponding function in frequency domain?

For example, I want to use fft to transform the simple function exp(-x.^2) defined in time domain. And the corresponding funciton in frequency domain is sqrt(pi).*exp(-k.^2/4). And I use the upper ...
23 views

I am working on a source separation problem and I have a logical mask that when applied to the STFT matrix, gives me expected results. The problem here, is that the mask is based on a spectral feature,...
4k views

Discrete wavelet transform; how to interpret approximation and detail coefficients?

I am trying to understand Wavelet transform. So far I have understood the basic theory of it. But I am not able to get my head around how to interpret both coefficients. I am using PyWavelets ...
127 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-...
99 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 ...
381 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 ...
379 views

Mixed time/frequency domain data

I'm afraid this might be a bit of an elementary question, but I'm afraid I'm a little new to this. I've got a system that measures a frequency spectrum to find resonant frequencies. It does this by ...
438 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 ...
271 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 ...
290 views

68 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 ...
56 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 $I$ ...
75 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 ...
81 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 ...
832 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 $$f_3(t) = \frac{f_1(t)}{f_2(t)}$$ ...
77 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{...