Questions tagged [time-frequency]

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18
votes
1answer
6k views

What's the difference between the Gabor and Morlet wavelets?

The Gabor wavelet is a kind of the Gaussian modulated sinusoidal wave (source)   Gabor wavelets are formed from two components, a complex sinusoidal carrier and a Gaussian envelope. (source) ...
9
votes
4answers
3k views

Why LTI system cannot generate any new frequencies?

Why $Y (\omega) = X(\omega)H(\omega)$ implies that an LTI system cannot generate any new frequencies? Why if a system generates new frequencies, then it is not LTI?
8
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1answer
948 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, ...
7
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2answers
28k views

Amplitude of the Signal in Frequency Domain different from Time Domain

How does the Amplitude of the Signal is changed when taking the FFT of a Signal, Have a look, The amplitude had changed from 2 to 30, and Here is my code for generating the above output, ...
7
votes
1answer
2k views

Doppler shift in time domain?

I have some clarifications required in this topic So initially I know that to shift a signal $X(f)$ by $f_0$ we need to take its inverse fourier transform and multiply it with a factor of $\exp(−j2\pi ...
7
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1answer
2k views

Match Filter in Time-Frequency domain instead of just Time domain. Redundant, or better?

Assume you have a signal, and within it, some pulses are present. A pulse is a simple tone. You know the pulses' duration and shape. (Let us assume that a pulse is made of a couple of cycles, and then ...
7
votes
1answer
283 views

What's the similarities and differences between Wigner transform and wavelet transform?

Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal. What are the similarities and differences between them? Could you give some ...
6
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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 ...
6
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3answers
19k 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 ...
5
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2answers
294 views

Why we need Frequency and Time information at the same time

The big disadvantage of a DFT is that it has only frequency resolution and no time resolution. This means that although we might be able to determine all the frequencies present in a signal, we do not ...
5
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5answers
3k 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\...
5
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1answer
572 views

How to Map CWT to Synchrosqueezed wavelet transform?

I don't understand the mapping time-scale plane to the time-frequency plane in synchrosqueezed wavelet transform, i.e. $(3)$. You can find the paper here. For the given signal of $x(t)$ and mother ...
5
votes
1answer
156 views

Possibility of temporal super resolution

I've been reading some papers in the context of super resolution in imaging and video (for example works by Michal Irani [1], [2] and so forth), and was wondering if a similar idea can be applied with ...
5
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2answers
537 views

Is Gabor uncertainty a feature of the Fourier transform, or of nature?

By Gabor uncertainty, I mean the principle of uncertainty as applied to signals — with the result that you can't have arbitrary time and frequency localization. By way of background to my question, ...
5
votes
4answers
436 views

Mixed time/frequency domain data

I'm afraid this might be a bit of an elementary question, but I'm afraid I'm a little new to this. I've got a system that measures a frequency spectrum to find resonant frequencies. It does this by ...
5
votes
2answers
251 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 ...
4
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5answers
3k views

Weird behaviour converting velocity to displacement

I'm trying to convert accelerometer data from accelerations to displacement, I assume that the initial velocity is zero and the initial position is also zero. Here's my code, ...
4
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2answers
662 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?
4
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1answer
711 views

Motivation for using gabor transform instead of fourier transform

I am trying to understand the motivation for the above question for signal processing and image processing? Can anyone answer this question, or provide me with resources for this?
4
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1answer
7k 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 ...
4
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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?
3
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3answers
354 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 ...
3
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2answers
746 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 ...
3
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2answers
8k views

What does it mean to combine signals coherently?

What does the expression 'combine signals coherently' imply?
3
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3answers
335 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?
3
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1answer
5k views

How does time shift correspond to phase change in a discrete signal?

I was watching this video where the presenter remarks: For a discrete signal, time shift corresponds to phase change in a discrete signal but not vice versa. I was trying to figure out how this ...
3
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1answer
59 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 $I$ ...
3
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1answer
465 views

What is the role of Freqency in Digital Images [duplicate]

Possible Duplicate: What does frequency domain denote in case of images? If we look deeply into Digital Images they are purely generated by the pixels distributed in rows and coloumn and the ...
3
votes
1answer
530 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

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 ...
3
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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 ...
3
votes
1answer
2k views

Find time lag between two time series

I am trying to find the time lag between two time series over t = [0,1000] using MATLAB (not that it matters). The first time series is simply t^2. The second is (t-15)^2 which is, of course, shifted ...
3
votes
1answer
259 views

Does Wigner-Ville distribution provide the highest resolution?

For linear time-frequency representation, the resolution is limited by Gabor limit. However, if interference is allowed, the resolution may be higher. What is the possible resolution in such a case? ...
3
votes
2answers
1k views

Why would you use DCT as oppose to DFT for detecting oscillation in a signal?

For my project, I needed to detect the primary oscillation frequency in a signal data. As I googled around, it turns out that DCT is the best tool to find this (http://www.mech.pku.edu.cn/robot/...
3
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1answer
214 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 ...
3
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0answers
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 ...
3
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0answers
190 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}^{\...
3
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0answers
79 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{...
3
votes
1answer
444 views

Mathematical model of equivalent-time sampling, the resulting unevenly spaced periodic signal, and its interpretation

I sample a continuous signal $s(T)$ over time. This leads to $s[t]$, which depends on several factors of which some are (pseudo-) periodic. I am interested in the effect of one such periodic factors ...
3
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2answers
797 views

what is continuous wavelet (cwt) ,wavelet packet (wpt) and stockwell (S-T) computational complexity?

What is computational complexity of continuous wavelet transform cwt ? What is computational complexity of wavelet packet transform ...
3
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0answers
279 views

Hints and helps to implement an accurate wavelet packet transfrom

I want to implement a Time-Freqency analysis by wavelet packets. I don't know what level and sampling rate should I use. I've tried different value for level(3,4,5,6,). but I couldn't get an accurate ...
3
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1answer
585 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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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 ...
2
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4answers
1k 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
4k views

Time-frequency representation of sound signal using Matlab

I am currently doing a project on sound signal processing by using MATLAB. I have a problem regarding creating the command line so that I can get a graph containing frequency by its time. But this ...
2
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3answers
639 views

Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)?

First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ...
2
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1answer
259 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?
2
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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 ...
2
votes
1answer
396 views

Time-Frequency Analysis of Big Data - Data Size Reduction: averaging the most appropriate method?

Explanation: I would like to analyse the data from an experiment, which investigates the performance of a mechanical component using sensors, that has generated 2000 CSV files. Each file contains 513 ...
2
votes
1answer
61 views

Why are the systems equivalent?

Why are those two systems equivalent? System 1:$$\boxed{x[n]}\longrightarrow\boxed{\uparrow 3}\longrightarrow\boxed{\downarrow 4} \longrightarrow\boxed{y[n]}$$ System 2:$$\boxed{x[n]}\longrightarrow\...