Questions tagged [time-frequency]

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1answer
50 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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3answers
107 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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0answers
27 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
31 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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1answer
27 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
38 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
24 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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0answers
11 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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0answers
20 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
89 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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0answers
17 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
861 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
98 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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0answers
34 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
715 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
37 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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0answers
33 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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2answers
125 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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0answers
26 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
162 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
196 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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0answers
2k 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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0answers
27 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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0answers
28 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
67 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
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 ...
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0answers
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 ...
0
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1answer
67 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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3answers
331 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
72 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
190 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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0answers
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
337 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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0answers
197 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
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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0answers
166 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
1k 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 ...
1
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1answer
623 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 ...
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2answers
340 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 ...
2
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1answer
149 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
431 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
711 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
2k 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 ...
1
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1answer
58 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 ...
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1answer
575 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
95 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
134 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
189 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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0answers
74 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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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 ...