Questions tagged [time-frequency]
The time-frequency tag has no usage guidance.
188
questions
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2answers
78 views
A Fast Power Grid Frequency Estimation Approach Using Frequency-Shift Filtering using numerical example
I have read the paper A Fast Power Grid Frequency Estimation Approach Using Frequency Shift Filtering.
I want to prove it using a numerical example, I have problem how to calculate the ...
8
votes
1answer
290 views
What's the similarities and differences between Wigner transform and wavelet transform?
Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal.
What are the similarities and differences between them? Could you give some ...
0
votes
1answer
23 views
Aliasing Issues in Sub Band Coding
The general structure of Sub-Band Coding (SBC) is shown below:
The diagram shows that after each of the analysis filters, decimation is performed by a factor M which corresponds to the number of ...
2
votes
1answer
42 views
What is the effect of a larger window size on “temporal resolution”?
I guess my question boils down to what "temporal resolution" means?
I'm taking a signal processing class right now and we're learning about DFT and windowing at the moment. We've learned ...
1
vote
2answers
42 views
Synchrosqueezed STFT phase transform
Synchrosqueezed STFT paper defines STFT phase transform as:
$$
w(u, \xi) = \xi - \frac{\partial_tS_{g}f(u, \xi)}{j2\pi S_gf(u, \xi)}
$$
which differs from synchrosqueezing original paper's (per CWT) ...
1
vote
1answer
36 views
How to accurately compute the Winger-Ville Distribution of an exponential
I am using MATLAB for this question so hopefully you can help me out.
I am trying to compute the Wigner-Ville distribution (WVD) of a sinusoidal signal defined as
\begin{equation}
x(t) = e^{-i\omega_0 ...
1
vote
1answer
65 views
Fourier transform of time division
I know that Fourier transform of $t^n f(t)= i^n \frac{d}{d\omega^n} F(\omega)$.
But does this work when $n<0$?
Is there any direct relation to compute the Fourier transform of $\frac{f(t)}{t}$?
0
votes
1answer
60 views
Recover frequencies from IQ samples
I have a set of IQ data. From those data I'm trying to get the amplitudes and the frequencies of my signal as I then want to plot them vs. time.
I am able to obtain the amplitudes by squaring both ...
0
votes
1answer
2k 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 ...
0
votes
0answers
31 views
Reconstructing signal from frames
Edit: Please treat code here as python-esque pseudo-code; it would syntactically fall closest to MATLAB or Python+numpy+scipy users.
If I have a signal in frames, and I want to put it back together - ...
0
votes
1answer
51 views
Why does alpha of 0.5 in detrended fluctuation analysis indicate randomness?
I'm trying to get an intuitive understanding of the different coefficients in detrended fluctuation analysis (DFA).
It is used to detect fractal patterns in time series and it yields a coefficient, ...
0
votes
2answers
62 views
Questions about MP3 bitrate conversions
I was trying to analyse the lossy compression of MP3 audio files through their Spectrograms and the results were something like this (where the upper is 80Kbps and lower is 128Kbps).
It is obvious ...
1
vote
2answers
136 views
How is wavelet time & frequency resolution computed?
Mallat gives analytic wavelet time & frequency widths/uncertainties as
$$
\begin{align}
\sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt
= s^2 \sigma_t^...
4
votes
2answers
699 views
Synchrosqueezing Wavelet Transform explanation?
How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?
2
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 ...
0
votes
1answer
919 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 ...
5
votes
2answers
253 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 ...
1
vote
1answer
282 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 ...
0
votes
1answer
102 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 ...
1
vote
2answers
47 views
DWT on short signals
I have signals with a very short rate of ~100e-6 seconds, sampled at 10MHz,so about 1k samples.
I am wondering, is there a practical limit to the usefulness of time-frequency methods concerning a ...
4
votes
2answers
2k 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
1answer
574 views
How to Map CWT to Synchrosqueezed wavelet transform?
I don't understand the mapping time-scale plane to the time-frequency plane in synchrosqueezed wavelet transform, i.e. $(3)$. You can find the paper here.
For the given signal of $x(t)$ and mother ...
1
vote
2answers
50 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 ...
0
votes
3answers
185 views
How do I time-stretch a signal from the frequency domain?
I have $FFT(signal)$, and want to find $operation$ such that $$IFFT(operation(FFT(signal),2)) = timestretch(signal, 2)$$
Where $timestretch$ stretches the signal in the time domain - maintaining the ...
0
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0answers
34 views
RMS and RMQ from PSD
From acceleration data I made a Power Spectral Density (PSD) and calculated the RMS via:
$$a_{RMS} = \left[\displaystyle\int_{f_1}^{f_2} a_{PSD}(f) df\right] ^{\frac 12}\tag{1}$$
Now, I want to ...
0
votes
1answer
64 views
Plotting a Time Frequency contour/colormesh plot of a Discrete Wavelet Transform
I have a pressure vs time data of a noise on which I wish to perform discrete wavelet transform.
I have divided my frequency range into 1/3rd Octave Bands and have calculated sound pressure level at ...
6
votes
3answers
19k views
Continuous Wavelet Transform with Scipy.signal: what is parameter “widths” in cwt() function? How do time-frequency?
I search to display a time-frequency signal with an original discrete temporal signal (sampling step = 0.001sec). I use Python and the library Scipy.signal. I use the function ...
2
votes
2answers
95 views
Defining an average in time for a density in time
I'm reading the text book "Time-Frequency Analysis" by Leon Cohen and I've made my way through a decent portion. There is however a conceptual issue I keep coming back to. The book states:
If we ...
-1
votes
1answer
102 views
A one-pole LPF (6 dB/oct) has a step response to $1/e$ amplitude of ${\tt time} = 1/(2 \pi f)$. What would the response time be of a 3 dB/oct filter?
I was instructed in another question here that if a one pole (6 dB/oct) low pass filter is fed a discontinuity (ie. going from 1 to 0) it will take ${\tt time} = \frac{1}{2\pi f}$ to reach $1/e$ ...
0
votes
2answers
25 views
What does following statement mean: “ Simulation was done at the rate of 12 samples per cycle of 50Hz a.c.”
I am very new to the signal processing world and i am currently doing a project of studying frequency components in electrical machines. I am simulating the system in PSCAD. But i need to simulate the ...
0
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0answers
13 views
What is the origin of the line shape in a Marginal Hilbert Spectrum
When calculating the marginal Hilbert spectrum of a discretely sampled harmonic oscillation (sine wave), I have found that the peak in the spectrum has a roughly Lorentzian line shape, albeit ...
0
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0answers
21 views
Why does the Marginal Hilbert Spectrum of an anharmonic oscillator have two peaks?
I've been looking at the marginal Hilbert Spectra of both the simple harmonic oscillator and the anharmonic Morse oscillator. I have found that while the SHO has a marginal spectrum with a single and ...
0
votes
2answers
101 views
How to avoid overtones in audio signal
I'm trying to make a program that catch and audio signal of a bass and show the notes that have been played. My program:
Gets the sound and put it in a double data type array. (48 000Hz, 16bits) ...
0
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0answers
19 views
Calculating the spectrogram of the center of pressure time series in human standing balance
I have some biomechanical data of a few subjects standing on a force plate. The center of pressure along the x and y axes was measured. The total time of measurement was 30s and the sampling frequency ...
0
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2answers
1k views
Obtain the frequency response of a time domain chirp signal
I have simulation data in the time domain and I need to represent them in the frequency domain.
The data have been obtained time integrating the following equation:
$m \ddot{x} + c\dot{x} + kx = A \...
0
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0answers
52 views
Varying speed of shaft Spectral Kurtosis
I want to perform Spectral Kurtosis (Kurtogram) on 10-second vibration signal of 25.6 kHz sample rate, where the shaft is varying in speed.
Will a preprocessing step of resampling the signal be ...
2
votes
2answers
1k views
Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain
My goal is to compute the Fourier of the product between two discrete time signals, y1 and y2. This can be done by computing the convolution between the fourier transform of y1, f1 and the fourier ...
1
vote
2answers
136 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(...
3
votes
2answers
2k views
Extracting Peak Frequencies Using FFT vs. Time Domain Peak Finding
I am trying to compare two processing algorithms that I believe should be producing very similar results. I am processing acceleration signals over the course of the day and we expect to see a ...
1
vote
1answer
60 views
Play with a Gaussian Random Set in the Frequency Domain to Obtain Desired Effect in the Time Domain
Please assume we have a set of 100 random numbers obeying Gaussian PDF in time-domain. Let's index them 1-100.
Within a time-accurate simulation, I apply four operations on this dynamic set every ...
1
vote
1answer
697 views
Comparison of Linear Convolution and N Point DFT
I am studying Discrete Fourier Transform currently and I have a doubt in that.
Consider two sequences $$\left\{1,2,3,4\right\}$$ and $$\left\{0,1,0,0\right\}$$ When I convolve them linearly, I get ...
2
votes
2answers
306 views
How Many Samples Are Identical In Linear and Circular Convolution Result?
Suppose we have two sequences $x[n]$ of length $L$ , and $y[n]$ of length $P$. If we are doing a $L$ length circular convolution between the two sequences ($L>P$), how many of the resultant samples ...
2
votes
2answers
895 views
Linear and Circular Convolution in Fourier Domain (DFT)
Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
-1
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1answer
799 views
Properties of Circular Convolution
Multiplications of time domain vectors of two signals is equivalent to convolutions in frequency domain and also use circular convolutions for when FIR filter design using window method in frequency. ...
0
votes
2answers
38 views
Can amplitudes be used to differentiate one signal from another?
I have use case, where there are lot of sensors placed under ground.The sensors give amplitudes each second.So my aim is to detect if some anomalous activity takes place at that point.
IF an activity ...
0
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0answers
50 views
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 ...
0
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0answers
28 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 ...
0
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1answer
181 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^...
3
votes
1answer
215 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 ...
3
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0answers
4k 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 ...
