# Questions tagged [time-frequency]

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### 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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### 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 ...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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### 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 ...
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### 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 $1/e$ ...
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 ...
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 ...
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 ...
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### 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) ...
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 ...
1k views

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### 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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### 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. ...
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 ...
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 ...
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 ...