Questions tagged [fourier-transform]
The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
1,567
questions
0
votes
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 ...
0
votes
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 =
3
votes
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 ...
0
votes
4answers
90 views
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 ...
0
votes
2answers
81 views
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 ...
0
votes
0answers
44 views
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=...
1
vote
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 ...
0
votes
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(...
0
votes
0answers
17 views
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? ...
0
votes
0answers
20 views
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 ...
1
vote
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 ...
0
votes
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 +...
3
votes
2answers
2k views
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 itā...
0
votes
1answer
41 views
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 ...
0
votes
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.
...
0
votes
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 ...
2
votes
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] - ...
1
vote
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 $\frac{f(t)}{t}$?
0
votes
0answers
29 views
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 ...
0
votes
0answers
67 views
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 ...
1
vote
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 ...
0
votes
0answers
23 views
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 ...
3
votes
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 ...
0
votes
1answer
44 views
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 ...
1
vote
0answers
21 views
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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.
...
11
votes
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 ...
0
votes
1answer
20 views
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 ...
1
vote
2answers
61 views
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:
$$w_j=\sum_{m=1}^{11}A_m\sin\left(\frac{mĻx_j}{L}\right)$$
where $A_m$ are the Fourier ...
0
votes
2answers
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 ...
4
votes
5answers
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 <...
-1
votes
2answers
76 views
How to plot thermal noise in the ātime domainā?
$P = 4kT$ (where $k$ = Boltzmannās 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 ...
2
votes
5answers
4k views
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 $e^{-j \omega t}$:
$$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...
0
votes
1answer
88 views
Calculating the magnitude spectrum and phase spectrum
From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$.
Then, I want to calculate its magnitude spectrum and phase spectrum.
The ...
0
votes
1answer
40 views
Does it make sense to express a given FT from 0 to 1 as a convolution?
I'm learning about Fourier transform, and was asked whether the following FT can be expressed as a convolution: $$X[k] = \sum\limits_{n=0}^{N=1} x[n]e^{-i\frac{2\pi}{N}kn}$$
There are two things I don'...
1
vote
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 ...
0
votes
0answers
34 views
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.
...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
1answer
41 views
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 ...
1
vote
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&...
3
votes
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)...
24
votes
6answers
130k views
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 ...
0
votes
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 ...
2
votes
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 (...
0
votes
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 ...
