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Questions tagged [time-frequency]

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1answer
40 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....
0
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0answers
14 views

Derivation of the reassigned STFT magnitude of a complex exponential

I have a complex exponential defined as $x(t)=Ae^{i2\pi f_{0}t}$ and its short time Fourier transform with respect to the analysis window, $g(t)$ is defined as, $$X_{g}(b,f) = \int_\mathbb{R} x(t+b)g(...
1
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1answer
67 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
16 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
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1answer
63 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
18 views

Filtering frequencies in diferent ranges in Python

I would like to filter frequencies: Alpha, Beta and Gamma. These bands have a relation with the task that I want to classify, I am using the Gumpy python tool which has a method to apply Butterworth ...
1
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0answers
54 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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0answers
10 views

How to implement freq convolution layer?

I am referring the paper https://pdfs.semanticscholar.org/31c7/4962122ba5fe1c469101b5bc2ae6d88c9c18.pdf. In the paper, for CLDNN network first layer is freq convolution. How to implement the same for ...
4
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2answers
518 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
41 views

How to make function in time domain after fft fit with the corresponding function in frequency domain?

For example, I want to use fft to transform the simple function exp(-x.^2) defined in time domain. And the corresponding funciton in frequency domain is sqrt(pi).*exp(-k.^2/4). And I use the upper ...
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0answers
15 views

time-frequency masking with shared properties between vector masks

I am working on a source separation problem and I have a logical mask that when applied to the STFT matrix, gives me expected results. The problem here, is that the mask is based on a spectral feature,...
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0answers
53 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 ...
1
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2answers
170 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 ...
2
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2answers
193 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
115 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-...
1
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1answer
207 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 ...
1
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1answer
148 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
499 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 ...
0
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0answers
563 views

How does the Scipy implementation of CWT actually work?

I'm trying to use the SciPy implementation of the Continuous Wavelet Transform to analyze EEG data. I am using The problem is that I have no idea what the width parameter should be. It says that it's ...
3
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1answer
339 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 ...
2
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0answers
87 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 ...
0
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1answer
76 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 $|n|\le N/2$. ...
2
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0answers
155 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
65 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 ...
3
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1answer
56 views

Is there a name for the procedure of taking the FT over separate consecutive small time-blocks?

Suppose we have a continuous time-interval $I=[a,b]$, and a signal $x \colon I \to \mathbb{R}$. A procedure that is sometimes carried out (e.g. when doing bispectral analysis) is to partition $I$ ...
0
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1answer
68 views

Basic sampling excercise - unsure of rationale informing np.arange parameters for time array

I'm extremely new to DSP, so I apologise if it's a very basic question. I'm having issues understanding the following exercise: "Create an array of 201 samples containing a sin wave with a frequency ...
0
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2answers
253 views

compensation for irregular timestep for 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
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1answer
3k views

scipy.signal.spectrogram

I want to do time-frequency analysis of a signal. So i decided to use spectrogram function from scipy. This function returns, three parameters f,t,Sxx. I am using below arguements: x : my signal fs : ...
2
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0answers
70 views

How to derivate in the frequency domain

I have two Time Domain functions, $f_1(t)$ and $f_2(t)$. I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
5
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1answer
144 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 ...
0
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1answer
627 views

Fourier transform of function division in time domain

$F_1(\omega)$ is the Fourier Transform of $f_1(t)$. $F_2(\omega)$ is the Fourier TRansform of $f_2(t)$. Can I obtain the Fourier Transform ($F_3(\omega)$) of $$ f_3(t) = \frac{f_1(t)}{f_2(t)} $$ ...
3
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0answers
75 views

Interpretation of instaneous time and instaneous frequency in time-frequency plane?

In this paper: Sparse time-frequency representations, Given signal $x(t)$, the time-frequency representation was got by Gabor transform and was denoted by $\chi(t,\omega)=|\chi(t,\omega)|\exp(\mathrm{...
0
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1answer
159 views

Why are analytic signals so important in Time-frequency analysis?

I am little confused about why we need analytic signals so bad in time-frequency analysis. What might happen if I use non-analytic signals to do time-frequency analysis?
0
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1answer
62 views

Dimensional analysis in the Morlet wavelet

I'm a complete beginner on signal processing, so please forgive the basicness of this question - but I'm very confused by this. Regarding the Morlet wavelet, Wikipedia says: The wavelet is defined ...
-2
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1answer
189 views

Finite moving average filter

I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....
2
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4answers
538 views

How to interpret the effect of different windows in short time fourier transform?

There are many categories of windows, e.g., rectangular, Gaussian, and triangular. What are their effects on STFT?
2
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1answer
295 views

Confused on the difference between the frequency spectrum of an entire song, and the frequency spectrum of a point in time

I am very much a beginner in this field - but find it really interesting. However I am a little confused on a certain area of knowledge. If I have understood correctly: At any point in an audiosignal,...
3
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1answer
3k views

Discrete wavelet transform; how to interpret approximation and detail coefficients?

I am trying to understand Wavelet transform. So far I have understood the basic theory of it. But I am not able to get my head around how to interpret both coefficients. I am using PyWavelets ...
3
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2answers
427 views

A system that perfoms Fourier Transform operation - is it an LTI system?

If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system? For if the input time domain signal can be represented as a linear ...
1
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1answer
153 views

Introduction to fast algorithms for time–frequency analysis

I had preliminary knowledge of digital signal processing from Oppenheim's Discrete-Time Signal Processing and is studying time-frequency analysis now. May someone suggest introductory reference (...
3
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1answer
2k views

Uncertainty principle - Duration bandwidth principle

In one of NPTEL courses about time-frequency analysis, the professor said that the duration bandwidth principle is $\sigma_t^2 \sigma_\omega^2 \ge \frac{1}{4}$. He added that the formula making use ...
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2answers
111 views

Filtering on a time signal

I am new to DSP, and am mostly self taught. I have a couple of questions, that may be too basic, but I couldn't really find an answer online. I have a signal obtained by plotting the motion of a ...
5
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5answers
2k views

Time-varying “impulse response”

According to many references [1,2], the time-varying "impulse response" can compute wireless channel output $y(t)$ at time $t$ using the following expression: $$ y(t) = \int h(\tau, t) x(t - \tau) d\...
3
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3answers
299 views

Motivation of time-frequency analysis

Can anyone give me an example of two signals with different temporal waveforms having the same Fourier transform (FT)? Would the inverse Fourier transform still be able to recover correctly each ...
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0answers
27 views

For extracting the characteristics of the signal what minimum duration should be considered?

Being non signal processing student I have a limited understanding of concepts. I have a continuous periodic bearing faulty signal of 10 seconds duration sampled at 12 kHz. So I have 120,000 ...
2
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1answer
193 views

Infinite extent of spectrum, but also in time in Oppenheim's Discrete Time Signal Processing?

In Oppenheim's Discrete Time Signal Processing there's on p. 323 no limited band in both time and frequency - wouldn't that violate the Heisenberg Principle?
1
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1answer
85 views

How to compute number of samples in 1 cycle of signal?

I have 3 signal sampled at 12 KHz frequency obtained from a motor rotating at constant 2000, 2020, and 2040 rpm. For 1 second signal recording I have 12,000 time samples. Depending on the frequency I ...
2
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0answers
128 views

Vibration signal analysis of non-stationary movement

my task is to develop a condition monitoring system of a machine module. For that I am using the vibration sensors placed on the machine housing. I want to focus on only one module of the machine, a ...
2
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1answer
176 views

Does the instantaneous frequency contradict the uncertainty principle?

The uncertainty principle states that there is a trade off between time and frequency. So, finding frequency components at specific time is impossible. However, the instantaneous frequency measure the ...
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0answers
298 views

How to choose notch frequencies for filtering line noise?

I'm using the function to filter out line noise at 60 Hz (and 120, 180 Hz) caused by electrical noise: ecogNotch In the case below I can effectively filter out the line noise with a notch filter at ...