Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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3answers
124 views

DFT coefficients meaning?

What "are" they? What's a sensible way to interpret the coefficients (and what isn't)? To pose specifics: DFT coefficients describe the frequencies present in a signal They describe the ...
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1answer
27 views

Partial column approximation error

Can someone help me understanf how to plot the next partial column in MATLAB: while N=2001 |M|<700 ak =
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2answers
163 views

Duality Property for DFT

I was watching a youtube video for the duality property for continuous time Fourier transforms, which shows that if Fourier transform of $x(t)$ is $X(\omega)$ then Fourier transform of $X(t)$ is $2\pi ...
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4answers
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what is the relationship between a spectrogram and the uncertainty principle heisenberg? [closed]

what is the relationship between these two things Perhaps more resolution in a spectrogram is equivalent to knowing more the position of the electron and less resolution is knowing the velocity of the ...
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Can I sample at Nyquist rate if I know that my samples are taken only at the signal's maxima or minima?

I know that in general the sampling rate, $f_s$, must be greater than twice the highest frequency of the signal, $f$. If I sample at the Nyquist rate, it can lead to the following: However, if the ...
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Why does upsampling in the frequency domain produces replicas of the signal in spatial/time domain [duplicate]

The experiment is the following: Given a 1d signal, e.g., a vector of values $f$. Let $F$ be its DFT, i.e., $F=fftshift(fft(f))$, shift is just to have DC centered. Then we upsample $F$ as $uF=...
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1answer
26 views

In computed tomography (CT), why is 'Inverse Problem of Radon transform' studied?

As I know, the Radon transform is a very important tool in CT by Beer's law. Thus, finding $f(x)$ of Radon transform $Rf(L):=\int_{L} f(x)dl(x)$ is helpful in CT. Nowaday, the Filtered back-projection ...
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1answer
30 views

expression for the FT of the frequency response of a system

I am trying to find an expression for the Fourier Transform of the frequency response of the cascade system seen here: Here is my approach: $(-1)^n = (-1)^{-n}$ $v[n] = x[n]e^{j\pi n}$ $V(e^{jw}) = X(...
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Is there anyway to find the frequency of DFT eigenvectors (basis) from its eigenvalues?

I've read this document which talks about the DFT. It describes that DFT bases are the eigenvectors of a circulant matrix. I know that every basis has a frequency in it, but I don't know what is it? ...
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Zero Padding in image reconstruction

I need to zero-pad the image for a better reconstruction but according to my project details, I will be given a Fourier-transformed image so can someone tell me how to pad the image in such a ...
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3answers
77 views

Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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1answer
35 views

Bluestein's algorithm to evaluate the DFT from $f_o$ to $f_o + k\Delta_F$

Briefly, the convolution between $x(nT) e^{-j2\pi f_o nT} e^{-j \pi \Delta_F Tn^2}$ and $c(nT) = e^{j \pi \Delta_F T n^2}$ multiplied $e^{j \pi \Delta_F T k^2}$ allows me to find the DFT $X(f_k = f_o +...
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Link between DFS, DFT, DTFT

My understanding of DFT is as follows For a signal $x[n]$ of finite-length, the DFT is DFS of the periodic extension, $\tilde{x}[n]$, of that signal $x[n]$ and also another way to view DFT is that it’...
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1answer
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What do different Cepstral or MFCC coefficients represent intuitively?

I understand the explanation for separating slow and rapid changing log spectral components but i need to understand: Why lower coefficients have higher and mostly positive magnitudes? Why Higher ...
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2answers
141 views

Distortion in sound after multiplying frequency spectrum by constant

I make a simple sound equalizer that operates in frequency domain and lets user to adjust frequencies in sound by using 4 sliders. The first one responsible for 0 - 5kHz, the fourth one for 15-20kHz. ...
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1answer
70 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
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5answers
322 views

DFT derivative property?

Does it have one? The continuous variant does, $f'(t) \rightarrow j \omega F(\omega)$ - but $jkX[k]$ definitely isn't it for DFT. To find it there must be a useful simplification of $\text{DFT}(x[n] - ...
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1answer
44 views

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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Power spectrum of modified process

Suppose there is a process $x(t)$ with power spectrum $$S_x(\omega)=\lim_{T\to\infty}\frac{1}{T}\left|\int_{-T/2}^{T/2}\mathrm{d}t\,e^{j\omega t}x(t)\right|^2,$$ ignoring the expectation value for ...
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Why does time-domain convolution correspond to frequency-domain multiplication? (visual)

I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...
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1answer
79 views

Fourier Transforms, Convolution, Cross-correlation: what is their physical unit exactly?

Let us assume we are talking about real, deterministic, electrical signals $x(t)$ and $y(t)$ (magnitude in Volts). There are different kind of Fourier Transforms. I made a table to summarize: NB: By ...
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Why is the Periodogram Used as an Estimate of PSD?

Why is the periodogram method as given by Schuster (1898) - which is not a consistent estimate of the PSD - still used, as opposed to consistent non-parametric methods for estimating the PSD like ...
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1answer
70 views

how to plot fft with imaginary and real part in 3d or calculate the degree of rotation

I would like to make a plot like 1 and see the real and imaginary part in a 3d space. I dont want to make exactly the same plot. for me it is okay if i see the peak for both signals shifted. it is ...
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1answer
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Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic

Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform. I can also calculate ...
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0answers
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Deriving Fourier Transform of Time-Windowed Discrete Signal

I'm trying to derive the Fourier Transform of a finite-length discrete signal to show the effect of windowing,e.g. spectral leakage and resolution, but I can't seem to arrive at the same answer. Just ...
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2answers
74 views

Correction of amplitude after zero padding for upsampling purposes

I have time sequence in which the data is sampled at 0.8 Hz. The data is related to chromatography (chemical analysis), that is why the sampling frequency is relatively low. The instrument cannot ...
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0answers
19 views

Morlet wavelet: DFT vs Fourier Transform

I find what seem to be contradictions between the two. "Morlet" defined here, and its Fourier Transform (FT) below it. DFT's imaginary component zeroes with large ...
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2answers
135 views

Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
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3answers
2k views

Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
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1answer
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Heterodyne modeling confusion in SDR

I've been reading this lab sheet which explains the signal processing math of the RTL-SDR radio dongle. http://www.eas.uccs.edu/~mwickert/ece4670/lecture_notes/Lab6.pdf In pages 5 and 6, the local ...
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How to determine the sine Fourier coefficients of discrete data?

The following relation gives me the measurements of interest $w$ at equally distanced locations $x_j$ in space: $$w_j=\sum_{m=1}^{11}A_m\sin\left(\frac{mπx_j}{L}\right)$$ where $A_m$ are the Fourier ...
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466 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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4k views

About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform). For common applications, usually we get a segment(length <...
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2answers
76 views

How to plot thermal noise in the “time domain”?

$P = 4kT$ (where $k$ = Boltzmann’s constant, and $T$ = temperature of the instrument ($K$)) And the mean voltage is thus, of course, $V^2/R = 4kT$ And the voltage is distributed as a Gaussian around ...
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5answers
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What does the exponential term in the Fourier transform mean?

We know that Fourier transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...
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1answer
88 views

Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
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1answer
40 views

Does it make sense to express a given FT from 0 to 1 as a convolution?

I'm learning about Fourier transform, and was asked whether the following FT can be expressed as a convolution: $$X[k] = \sum\limits_{n=0}^{N=1} x[n]e^{-i\frac{2\pi}{N}kn}$$ There are two things I don'...
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1answer
559 views

Relation between two k-spaces phase-frequency and spatial frequencies in

When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same. Axes are the two spatial frequencies. This images is directly fourier-transformed into the ...
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0answers
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How much zero padding I should do to an audio signal before fft?

I was working on project and I need to do fft to my audio signal. I was going through a code and found following line. Can anyone explain me the line of code. ...
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2answers
197 views

Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
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1answer
47 views

Determine reflections from received signal

I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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1answer
37 views

Applying fourier transform twice (DSP course)

I stumbled upon a question in a DSP course (coursera) which I don't understand, shown below is a screenshot of the question and answer. The part which I don't understand is circled. Why is it equal ...
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2answers
60 views

What is the effect of wiping the right half of Fourier Transform bins?

I'm trying to change the pitch of a signal using a Fourier Transform (FFT) followed by an Inverse Fourier Transform (IFFT). I've found many examples, some of which zero out the right half of the real ...
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1answer
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Palmprint Identification - Why do we align the images before we use the Fourier Transform?

I was reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm. The first step in their ...
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1answer
267 views

How to calculate the Fourier transform of a mean filter in Matlab?

In Matlab, how can I calculate the discrete-space Fourier transform of a mean which takes the average of 4 adjacent points, with this kernel $$\begin{pmatrix} 0 &1& 0\\ 1 &0&...
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1answer
263 views

Applying duality property to fourier transform of unit step function

For Continuous time aperiodic signals, the duality property of Continuous Time Fourier Transform (CTFT) is following $$\mathscr{F}\Big\{x(t)\Big\} = X(f), \qquad\text{then} \quad \mathscr{F}\Big\{X(t)...
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6answers
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Difference between discrete time fourier transform and discrete fourier transform

I have read many articles about DTFT and DFT but am not able to discern the difference between the two except for a few visible things like DTFT goes till infinity while DFT is only till N-1. Can ...
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1answer
490 views

Why the energy is a good feature extraction for detect disturbances in signal processing?

To detect disturbances in signal processing a common step is to extract signal characteristics to analyze them, among these characteristics it is recommended to use the signal energy. Why energy is ...
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1answer
105 views

Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
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1answer
122 views

How to make low pass filter using frequency sampling method?

https://www.allaboutcircuits.com/technical-articles/design-of-fir-filters-using-frequency-sampling-method/ So there is two main equation: I wish to filter out frequency $\le 10000Hz$, for example. So ...

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