Questions tagged [time-frequency]
The time-frequency tag has no usage guidance.
175
questions
1
vote
1answer
44 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 $\frac{f(t)}{t}$?
2
votes
1answer
5k 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
890 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
220 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
278 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
3answers
100 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
votes
1answer
66 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 ...
0
votes
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 ...
0
votes
0answers
24 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
30 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 ...
0
votes
1answer
31 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 ...
6
votes
3answers
18k 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
93 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
87 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
23 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
votes
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 ...
0
votes
0answers
19 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
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) ...
0
votes
0answers
16 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
votes
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
votes
0answers
33 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
736 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
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(...
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
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 ...
1
vote
1answer
611 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
248 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
624 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
votes
1answer
642 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
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 ...
0
votes
0answers
30 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
votes
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 ...
0
votes
1answer
157 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
195 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 ...
2
votes
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 ...
0
votes
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 ...
1
vote
0answers
27 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-...
8
votes
1answer
922 views
Least Squares Re Synthesis of Short Time Fourier Transform (STFT)
Working with my own MATLAB implementation of the short-time Fourier transform (STFT), I've managed to write code for the analysis step where a 1D time-domain signal $s[t]$ is progressively windowed, ...
1
vote
2answers
591 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 ...
-1
votes
1answer
65 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 ...
0
votes
0answers
37 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 ...
1
vote
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 ...
3
votes
3answers
330 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?
1
vote
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
votes
1answer
71 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....
1
vote
1answer
182 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 ...
1
vote
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 ...
1
vote
1answer
321 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) = \...
1
vote
0answers
192 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 ...
