Questions tagged [fourier]

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Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
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3 votes
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294 views

Points of interest in a spectrogram

We have several audio tracks, all of which are different versions of the same track under one type of distortion: the speed of the track is increased by a constant factor K (hence frequences are ...
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What is the variance of DFT of Fourier coefficient of difference of a vector of white noise?

Consider $\big\{x[0], x[1], \ldots, x[N-1]\big\}$. Suppose, \begin{cases} x[n] \sim \mathcal N\left(0, \sigma^2\right)\\ \big\langle x[n], x[n-1]\big\rangle = \frac12 & \forall \ n\\ \big\langle x[...
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2 votes
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68 views

Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
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  • 121
2 votes
1 answer
359 views

Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ...
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2 votes
1 answer
779 views

How to estimate covariance matrix using Fourier representation?

So, I have multidimensional time-series $X \in R^{(d \times T)}$, and I want to determine the covariance matrix of that signal in a specific frequency band. I might filter the signal to that specific ...
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1 vote
0 answers
56 views

Confusion regarding STFT phase vocoder-based pitch shifting

I'm currently working on a phase vocoder implementation based on the Short-Time Fourier Transform; it's heavily based on the models described here and here. I have successfully completed the analysis ...
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1 vote
0 answers
51 views

How to find sharpness of an image?

I have a rather difficult image processing image. I would like to rank order a set of images I have by their sharpness. The issue is the images themselves are not of the exact same thing. Usual ...
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1 vote
0 answers
40 views

How to downsample a fourier transformed signal?

I have a signal of length 100000 timestamps sampled at a frequency of 25kHz. First I apply a high pass filtering at (300Hz) and then do the Fast Fourier Transformation. Then the absolute values are ...
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38 views

When plotting the cosines of the phases of some sensors, I got an interesting plot

I have a laser that I modulate at some frequency, typically 1250 Hz. I have a sensor that tracks what happens inside a reactor when it's illuminated. I am doing Fourier analysis on both the laser ...
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  • 103
1 vote
2 answers
241 views

Resampling with and without replacement for estimating significance of spectral components

In order to test the significance of spectral components, it seems reasonable to randomly sort the data in order to destroy all the serial correlations / spectral order e.g. 100,000 times, and then ...
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1 vote
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Flat top sampling to a step shape signal

Flat Top Sampling During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat i....
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Is there a way to go from a set of (F/D)FT values to FIR coefficients?

I'm not yet well educated on the DSP subject, but I've initiated a project where I will do some audio filtering. My intuition tells me that there is a link between the coefficients of a FIR filter and ...
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1 vote
0 answers
147 views

Creating synthetic frequency domain box filter vs 4 pixels in corners

Creating two 10x10 black images. 1st image, adding a 2x2 white box in the middle (Low pass filter). 2nd image, adding 1 pixel in each of the corners. Then performing the following steps in that order:...
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1 vote
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580 views

Using Fourier Transform on Gyroscope

The original idea is to calculate distance from accelerometer input. However, accelerometer reading also contains the gravitational values, thus to remove gravity, I tried using Gyroscope. The idea ...
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  • 111
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789 views

Extraction of fundamental signal information-Fourier full cycle algorithm

After filtering my noisy input signal using an anti-aliasing and FIR filter, I now wish to get the basic signal information (peak voltage and impedance; $R$ and $X$) from the pre-filtered as well as ...
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1 vote
1 answer
320 views

Averaging magnitude squared coherence across multiple time series

In a previous post, A. Donda had suggested that, in order to calculate the average magnitude squared coherence of more than one pair of time series (e.g. y1 and x1, and y2 and x2), one ought to follow ...
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0 votes
1 answer
25 views

Given the Fourier Transform of a continuous signal how can I sketch the sampled signals discrete time fourier transform

I am given the frequency response for a continuous time signal X(jw) = 2 at w=0 and 0 at w = -10000pi and 10000pi. Looks like a triangle. I am told to sketch X(e^jw) the frequency response of a ...
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0 votes
0 answers
23 views

What can I do to improve the sound of a signal?

I want to improve the sound of my signal, I know I can do it by increasing or decreasing the amplitude of the signal itself. Are there any other ways to do this? How can I apply the Fourier transform ...
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0 answers
39 views

What happens if I register my entry?

Taking as an example that I want to record my voice. How does it appear in the frequency spectrum? Can I also view it on other spectra?
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52 views

Fourier Transform: $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$

I'm currently studying Fourier Transforms and do not understand the Fourier Transform of $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$ My solution states that it is $X(\omega)=\frac{2}{2\pi}(-j\pi[\delta_0(...
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29 views

What is the trigonometric form of the discrete-time Fourier series or inverse discrete Fourier transform?

As we know, the continuous-time Fourier series (CTFS or just FS) has three forms: the trigonometric, the amplitude-phase or compact trigonometric, and the complex exponential. I've found formulas for ...
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  • 103
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0 answers
89 views

Approximation of Periodic Parabolic Function by Fourier Series!

I've just tried to approximate the periodic-parabolic signal by Fourier Series. I know, this sounds a bit strange. I am just trying to figure out relationship between Fourier Series and Taylor ...
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0 votes
0 answers
63 views

Gabor uncertainty and time-frequency resolution

I have a question about Gabor's uncertainty theorem, and how it relates to time and frequency resolutions. As I understand it, Gabor's uncertainty theorem states that the standard deviations of a ...
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  • 101
0 votes
3 answers
225 views

Convolve with a box filter in time domain

To low pass filter a signal, we have to convolve it with a sinc function because it's the same as multiplying the Fourier transform of the signal with a rect function, resulting in the high frequency ...
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0 votes
2 answers
184 views

Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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74 views

Fourier transform and energy of a convolution

Hi guys i have to find the fourier transform of the convolution: $$ sinc(t/2T)*\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) $$ i was thinking of express the summatory as : $$\sum\limits_{n-\...
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0 answers
43 views

Find CT Fourier transform of $ \left[ \frac{ \sin(\pi ~ t) }{\pi ~t} \right] \left[ \frac{ \sin(2\pi ~ (t-1)) }{\pi ~(t-1)} \right] $using properties

Use properties of Fourier Transform to solve the question. The question is in the imgur link below. I got $f_t$ of $\frac {sin(pi \cdot t)} {pi \cdot t}$ as rectangular pulse with value $1$ from -pi ...
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0 answers
123 views

Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?

Please, check the following discrete periodic sequence when the period $N=2$. $x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$ $..., x[0]= 1, x[1]= -1, x[2]= 1, x[3]= -1, ... , N=2$ According to my ...
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0 answers
38 views

$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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0 answers
39 views

frequencies in frequency spectrum with no correlation together

I have a lack of understanding of the following questions: If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
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47 views

Short Time Discrete Fourier Transform to detect time dependent changes in a frequency of interest & Filter

I am working in matlab to compute the fourier relative phase of two signals as per https://sci-hub.tw/10.1123/jab.2017-0250 I have identified the fundamental frequency ($f_1$) for the signals (1.7 Hz)...
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0 votes
0 answers
91 views

express pass band filter as sum of low pass filter

I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
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0 votes
0 answers
338 views

Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$ x(t)=\operatorname{sinc}(t) $$ and $$ s(t)=x(t-T)$$ and I found that ...
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0 votes
0 answers
213 views

Range Doppler Maps

I would like to understand from a high point of view how these maps are computed. On the y-axis we have m/s and in the x-axis the range. I read something about the Fourier transform etc, but I don't ...
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0 answers
213 views

DFT truncation of signals

How can I calculate 8 point DFT of signals whose length is less then 8 ( say 2,4) then what will I assume other members in formulae "0" or rotation or keep repeating the same two numbers Consider I ...
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0 answers
89 views

how to calculate a SNR?

i had some question.i have do some some filtering FFT using a matlab program.but,i need to compared the original signal,noise signal,and filtering signal based on SNR.but i dont understand how to ...
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0 votes
0 answers
456 views

Filtering out different narrow-band frequencies at once

I have asked a closely related question on SO at https://stackoverflow.com/questions/55168460/python-implementation-for-filtering-out-multiple-distinct-narrow-band-frequencie but I am still unclear ...
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0 answers
94 views

Fourier decomposition in Matlab

I am doing a Fourier decomposition of sea level series ( to find out one particular contribution within the sea level height). it should be applied subsequently on shifted (by one hour) windows of 96 ...
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0 votes
0 answers
62 views

From Fourier (k space) to wavelet domain in MRI sensing

In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
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0 votes
0 answers
299 views

Equation for impulse train

I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both $1$ – so that $f(x)$ has value $1$ at $x = 1,2,3,4...$ and $f(x)$ has ...
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0 votes
0 answers
116 views

Confusion in understanding the Proof of DTFT

While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps. $$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n}$$ $$ a_k= \frac{1}{N} \sum_ {...
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45 views

ًWhy we use fourier transform in most of spectrum estimation approaches?

I wonder why in all spectrum estimation techniques, the analysis depend on the Fourier transform? Why not deal with the signals in time domain?
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239 views

Most efficient phase linear x4 resampling algorithm

I'm working on a program in which I need to do the following about 20 times for each block of audio: - Upsample from 192 to 768 kHz (x4) - Clip - Downsample back to 192 kHz (/4) What I'm using now: ...
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0 votes
0 answers
139 views

increase the # of points in a DFT, increase the processing

I have a question which is closely related to this one: FFT Processing Gain ^that discussion is a bit general so I want to ask a very objective question to see if I can apply that knowledge: If I ...
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0 answers
127 views

understanding windowed fourier ridges

I am studying windowed Fourier ridges for my project. I know that it computes the instantaneous frequencies and amplitudes from the spectrogram. But I don't really know how it relates to signal ...
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-1 votes
1 answer
104 views

Inverse discrete Fourier transform or inverse Fourier transform of composite function?

I collected spectrometric data which produced a graph with the intensity of each frequency of light. What more do I need to perform an inverse fourier transform of this data? Should I attempt an ...
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-1 votes
1 answer
167 views

DFT Signal DFT Length N , FFT

If we sample a signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequency of Fs = 8Hz, is it right that the length of the data should be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
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-1 votes
1 answer
51 views

Why do we scale bins in FFT in this code?

Hi I am learning FFT I am confused about this bit of code: what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you ...
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-1 votes
1 answer
95 views

Receiver function, frequency domain deconvolution not giving logic results

I'm working on some code for receiver function method in seismology. For anyone one not into the topic, it's just a deconvolution of two time series (seismograms). This can be done in the time domain ...
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