Questions tagged [time-frequency]

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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 $I$ ...
0
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1answer
115 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 ...
1
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2answers
603 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 ...
2
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1answer
6k 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
156 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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2answers
222 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
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1answer
2k 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
78 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
226 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
92 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
394 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....
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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
485 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,...
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 ...
3
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2answers
681 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
165 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
127 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
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\...
3
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3answers
348 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
30 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
253 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?
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1answer
318 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
183 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
218 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
424 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 ...
0
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1answer
526 views

Time position in STFT output

How can I understand in which time position in STFT function output am I? For example, if I have 3987 time frame in the output of STFT, my window length is 625 (hamming), my hop size is 125 and the ...
0
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3answers
526 views

BIBO stable LTI system frequency response for this input signal?

For an LTI system with bounded input and bounded output, I have the input $$x(t) = 5 + \cos(12t+\pi/4)$$ and output $$y(t) = 6\sin(12t)$$ It is said that the magnitude of the frequency response $|H(...
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1answer
126 views

Making a mesh out of the parameters from a STFT

I do not possess much knowledge about signal processing, so i hope to do a find an answer. I am reading a wav-file and then apply a fft on it. In theory, i think i have a 3 parameters i can use. Time ...
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1answer
1k views

Combining 2 sinusoids of equal amplitude with different frequencies into 1 new “wave”

This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave ...
0
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1answer
1k views

Inverse a frequency response

I haven't recorded a precise impulse response, but I have carefully written the attenuation/boost of a recording chain for every third of octave: ...
0
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1answer
2k views

What is the instantaneous frequency of this signal

Suppose we have the signal $x(t) = \cos(\pi t) + \cos(\pi t^2) + \cos(\pi \cos(\pi t))$ How can I find the formula which gives the instantaneous frequency $f(t)$?
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0answers
153 views

Feature recognition within a single song

I want to write an algorithm in C++ which is capable of identifying specific features within a single song, e. g. the sound of a drum which is played 100 times during 5 min. State of the project So ...
2
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1answer
385 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 ...
0
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1answer
2k views

Comparing PSD two signals of different length

I have two time signals A and B which are of different length, length(A) < length(B). Now I calculated the cumulative PSD of both signals. What is the best way to compare this result? If I am ...
0
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1answer
388 views

How to extract features from nonstationary signal using SVD (singular value decomposition)?

I am trying to extract features from a nonstationary signal (frequencies and time locations). For this purpose, I computed a wavelet transform (complex morlet) of the signal in MATLAB and obtained the ...
0
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0answers
128 views

Any examples of analysis in time domain to extact information

I am sending a 20Khz signal from my phone and capturing all the signals while doing exercise above it. Here I have a signal of a person doing "hand scissors exercise" I am doing analysis on how many ...
0
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1answer
269 views

Beginner's question on LPF, Need for Sinc and windowing [duplicate]

As a student who has never constructed any real world DSP application, I am inclined to ask the following. Convolution in time domain is multiplication in frequency domain. For low pass filtering, ...
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1answer
773 views

Shift property of the Short-term Fourier transform (STFT)

Properties of STFT (Short-term Fourier transform) say that it preserves time shift up to modulation. Does it mean it is sensitive to time-shift in signal?
2
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1answer
58 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\...
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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?
2
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2answers
252 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
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2answers
1k views

Compressing a time-domain signal in the frequency domain Matlab

I'm new to frequency domain analysis. Let's say I have a frequency domain representation from a time domain signal. What I want to do is taking frequencies with a low amplitude out of this frequency ...
0
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1answer
126 views

Confusion with regards to units in Sinc pulse

I am currently reading a section in the Handbook for MRI Pulse Sequence book where it says that the time-bandwidth product for a SINC pulse is given by: $$ T \Delta f = Z $$ where $T$ is the length ...
0
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2answers
410 views

Is this graph of Wigner-Ville distribution OK?

I am studying some code for smoothed Wigner-Ville distribution. update 3- solution, graph was over amplified in a 2d overdrive/oversaturation effect. if i divide by 20 only a line is visible. Update ...
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0answers
145 views

Does MATLAB have a FM discriminator [closed]

I'm wondering if MATLAB communications or DSP toolboxes has a FM discriminator? If so, what is the name of the function/object?
2
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1answer
666 views

Lowpass filter impulse response in frequency domain

A Linear Time-Invariant system with impulse response $h_1[n]$ is an ideal lowpass filter with cutoff frequency $\omega_c =\pi/2$. The frequency response of the system is $H_1\left(e^{j\omega}\right)$. ...
2
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1answer
8k views

Matlab signal processing removing white noise from signal

What is the way to address the removal of white noise from a signal? Extra Details Hi I also agree the details are as follow: ...
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1answer
5k views

How does shifting a signal in the time domain affect its frequency domain?

Suppose the signal is shifted by dt (signal 'starts' later, say after 1s instead of 0s), does that correspond to a positive or a negative phase shift df in the frequency domain? There are certainly ...
0
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1answer
896 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 ...