Questions tagged [time-frequency]

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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 ...
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2answers
88 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 ...
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1answer
50 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 ...
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1answer
39 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 ...
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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 - ...
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2answers
45 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) ...
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1answer
60 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, ...
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2answers
188 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^...
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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 ...
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2answers
872 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?
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2answers
51 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 ...
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1answer
69 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 $\frac{f(t)}{t}$?
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223 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 ...
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37 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 ...
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1answer
87 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 ...
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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 ...
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1answer
77 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 ...
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2answers
26 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 ...
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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 ...
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22 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 ...
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1answer
111 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 $1/e$ ...
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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 ...
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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 ...
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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) ...
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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 ...
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2answers
938 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 ...
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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 ...
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52 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 ...
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139 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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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 ...
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1answer
187 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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222 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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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 ...
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31 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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36 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
106 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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1answer
3k 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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23 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
128 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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340 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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81 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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1answer
260 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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19 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
402 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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233 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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2k 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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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?
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192 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
2k 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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1answer
712 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 ...