Questions tagged [fourier-transform]
The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
1,164 questions
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How to custom optimize cuFFT for a mini batch of multi-channel images?
I am reading a paper, which has the following paragraph.
Current GPU implementations of the FFT such as cuFFT are designed to
parallelize over individual transforms. This can be useful for
...
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Performing inverse DFT after taking conjugate of the result of DFT
The following is a question I got in my school assignment.
Pick an image and follow the operations
Multiply image by (−1)x+y.
Compute the DFT.
Take the complex conjugate of the ...
2
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1answer
31 views
Performing DFT twice on an image. Why am I getting an inverted image? [duplicate]
I was asked to perform DFT on an image twice as a part of my school assignment. Why am I getting a blurry inverted image when I perform DFT on an image twice? Sorry, I'm new to image processing and ...
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1answer
20 views
Inverse Laplace transform of two-sided and one-sided Laplace transform
As I read in Wikipedia, there are two types of Laplace transforms
One-sided Laplace transform: $F(s) = \int_{0}^\infty e^{-st} f(t) dt$
Two-sided Laplace transform: $F(s) = \int_{-\infty}^\infty e^{-...
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Fast Fourier Transform analysis for EEG signals [on hold]
Some tools like MNE are really useful for EEG signals, but for my dataset (DEAP dataset) for Python, is not compatible.
The shape of the data is the next:
Data: (40, 40, 8064) (Trials, Channels, ...
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Frequency Domain - Meaning [duplicate]
I'm new in digital signal processing and having hard time understanding this. By Fourier Transform I mean Discrete Fourier Transform as it's the only one I'm learning.
As far as I know Fourier ...
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Intuition behind FT of Dirac Comb [duplicate]
What is the intuitive explanation behind a dirac comb having a dirac comb as Fourier transform? How to calculate this is clear, but I cannot picture why this intuitively makes sense.
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Difference between the DTFT and DFT [duplicate]
I know this question has been asked before. It is, however, so confusing, that I'd like to give this another try:
I have come across the following 2 definitions of the DTFT:
So, the first line is the ...
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27 views
system function $H(\omega)$ relationship to odd and even components of h[n]
What qualities of $h[n]$ are necessary for:
$$
H(e^{j\omega}) = DTFT\{h_{even}[n]\} + j\ DTFT\{h_{odd}[n]\}
$$
Do all real / causal h[n] have the property that:
$$
H(e^{j\omega}) = DTFT\{h_{even}[n]...
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2answers
41 views
Zero-padding, energy conservation
When calculating the FT of a signal, and the FT of that same signal but after having applied zero-padding to it, should't the amplitudes of the FT of the zero-padded signal decrease with respect to ...
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How to get a scale bar of an FFT image of a TEM picture (ImageJ)? [closed]
I have a Transmission Electron Microscopy (TEM) image with a known scale (say 10 nm).
I performed FFT in ImageJ and the image looks good, but there's no scale bar. How do I get the scale bar for the ...
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Use 2D FFT to replace 2D Discrete Fourier Transform (MATLAB)
I met a problem. I ran a code to implement the 2D discrete Fourier Transform, here is the code:
...
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1answer
25 views
Finding delay parameters for watermarked signal
I have a watermarked signal WATERMARKED SIGNAL
And the actual watermark WATERMARK
In Matlab, I need to find out the delay parameters $d_i$ which can be considered as the embedded
information.such ...
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0answers
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How to find “The complex Fourier coefficients $X_n$”
In the picture I have the question with my attempt , I could find everything without problem but the 3rd branch's asking about $X_n$ (Fourier coefficients ) since I have $X_3$ and $X_4$ are equal 0 , ...
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1answer
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Audacity Spectogram view: how to see exact frequency and intensity under the cursor?
In the Spectogram view, simply clicking anywhere with the selection tool gives a vertical line to the top ruler, and shows at the bottom the exact sample, H:MM:SS, or other time coordinate you'd want.
...
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1answer
33 views
Sampling: How should I sketch a signal spectrum?
As revision, I am going through Signals and Systems, and in Section 7.1the authors are sketching representative spectra for x(t) and ...
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Convolution of signals sampled on a logarithmic grid
Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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31 views
Lowpass-filter necessary before DFT?
I'm trying to distinguish eletrical engines by the magnetic field they create. I have no idea whether this is a smart idea, it's possible at all, whatsoever. However it brought me to a basic question ...
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Correspondence between spatial frequency and pixel position
I have a very basic image processing question for which I have not been able to find an answer so far:
On several occasions I have encountered descriptions of image filters given in the frequency ...
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1answer
35 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
29 views
Confused about Fourier transform output
I am new to signal processing, so I did a fourier transform on a frame of 200 samples with NFFT = 512 and then I took the absolute value :
I am trying to understand these values on the output, are ...
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Burst Deblurring algorithm - Understanding the results
I've attempt to implement the algorithm from the paper "Burst Deblurring: Removing Camera Shake Through Fourier Burst Accumulation".
The main idea is to take several frames of the same scene, each ...
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42 views
Mirrored Spectrogram Mp3
First of all sorry if this is a stupid question, but I am an absolute beginner in this field and have been trying for days now.
I'm working on a java program that uses fft to analyze audio files.
To ...
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1answer
31 views
What is exactly Power Spectrum Density? [closed]
In papers or textbooks, I have found several different definitions of PSD. I think I understand the meaning of PSD and all these papers or textbooks agrees that PSD and Fourier Series share a ...
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1answer
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Correct form of discrete-time Fourier series representation
As I see in this slides, Fourier series representation for discrete-time signal $s[n]$ with period $N$ is $\sum_{k = 0}^{N-1} c_k e^{j2\pi k n / N}$
According to Wiki, Fourier series representation ...
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1answer
40 views
Relationship between Bandwidth and Bit Rate
In one of my classes I have learned that if we look at transmitting a binary signal with ASK, we can get the bandwidth (i.e. the width of the main lobe in the frequency domain) with BW = 2 * Fb, where ...
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Is it possible to recover the original signal from an LC circuit?
I'm using some photo detectors called Silicon Photo-multipliers (SIPMs) which produce a signal like the following:
Now, I take this signal and pass it through an LC circuit to get the following ...
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0answers
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A time limited gaussian that has a bandlimit?
I am currently reading the paper Factored Axis-Aligned Filtering for Rendering Multiple Distribution Effects, which uses signal processing in its theory. There is one part that I do not understand. It ...
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1answer
27 views
Fourier Series Representation of Continuous-Time Periodic Signals [closed]
As a novice in signal processing, I have been going through Signals & Systems by Oppenheim to try and understand how continuous time periodic signals are represented by Fourier series coefficients....
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1answer
24 views
Deconvolve a FIR-filter using limits? Or: Are limits distributive with the inverse fourier transform?
Given $y[n] = f[n] * h[n]$ where $y[n]$ and $f[n]$ are two one-dimensional discrete signals that are given, find out:
if $h[n]$ is a FIR-filter
if it is a FIR-filter, what its kernel is.
Obviously, ...
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2answers
63 views
Comparing FFT for increasing time intervals in a signal
Assume a dataset where the rows represent signals: each signal $s$ is sampled at a sampling rate $f_s$ and available as an array of common length $T$. For an increasing sequence of integer times $t_i &...
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2answers
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What is the DFT of DFT of discrete signal [duplicate]
What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
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1answer
71 views
Can a Fourier Transform exist even if the j$\omega$ axis is not in the Region of Convergence in it's Laplace Transform
A couple of confusions have been occurred. The Signal I'm considering is f(t) = sin(t)*u(t)
Fourier Transform of it can be derived.
$-i \pi (\delta (\omega -1)-\delta (\omega +1))$
According to my ...
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1answer
22 views
finding energy content of signal from “energy spectral density” function
from "Signals and Systems Demystified", 2006, page 142, Example 6-3: (http://www.gatestudymaterial.com/study-material/signals%20and%20systems/text%20books/SIGNALS%20AND%20SYSTEMS%20BY%20DAVID%...
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Determine 3 most dominant frequencies in a signal, PSD or just the absolute value of a Fourier transform?
I have a noisy ECG signal recorded for 5 minutes. My goal is to determine heart rate every 2 seconds. To find out 3 most dominant heart rates (Beats per minute) in a 2s-signal should I calculate its ...
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Power spectrum of a signal time-shifted by a stochastic delay
I'm trying to analytically compute the power spectral density (PSD) of a stochastic noise, say $p(t)$, which is time-shifted by a delay which is the sum of a constant delay $dT$ and a stochastic part $...
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2answers
40 views
Fourier-Analysis of Stationary Random Signals
Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated.
For such a signal, how can we determine ...
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1answer
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DFT of Transient vs. Analytical Solution
I'm trying to compute the Fourier Transform of a lightning impulse waveform. The python code I'm using is below. The problem that I am running into is that the magnitude of the DFT and the magnitude ...
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1answer
64 views
Limitation on the shift theorem of DFT due to frequency resolution?
The shift theorem states that shifting a sine wave in time domain by t is equivalent to multiplying the corresponding DFT coefficient of the signal by a complex exponential e^(-jwt). Described by the ...
2
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1answer
37 views
IDFT of $Y[k]=2X[k]$ for even $k$
If the 16-point DFTs of $x[n]$ and $y[n]$ are given as
$Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I ...
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Fourier transform of $e^{-at}\cos(\omega_0t)u(t)$
I am solving a question of Fourier transform which is:
$$ e^{-at}\cos(w_0t)u(t) $$
What I have done is:
$$ e^{-at}\cos(w_0t)u(t) =\frac{1}{2} e^{-at}e^{jw_0t}u(t)+ \frac{1}{2}...
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1answer
44 views
Is the following property true?
I was looking at a solution of a Fourier Transform question and following property was used, if:
$$ x(t)\rightarrow X(jw) $$
then:
$$ e^{jw_ot}x(t)\rightarrow X(j(w-w_0)) ...
1
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1answer
21 views
Linearity with Difference Period in Fourier Transform
I know that a system is linear if it satisfies
$$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$
for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$
But what if $x(t)$ ...
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1answer
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How to calculate the Fourier transform of a mean filter in Matlab?
In Matlab, how can I calculate the discrete-space Fourier transform of a mean which takes the average of 4 adjacent points, with this kernel
$$\begin{pmatrix}
0 &1& 0\\
1 &0&...
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inaudible part of signal in MFC transform
MFC transform eventually captures a good portion of the humanly intelligible part of audio signals. I was wondering at which steps of the transform is the inaudible part of the signal rejected? Is it ...
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1answer
51 views
Quite confused with Fourier Analysis results
So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve
$$
f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t)
$$
...
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0answers
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Horizontal artifacts in RFFT spectrogram
When displaying the spectrogram of one particular file I analyze I am shown with these strange artifacts like there is a lot of high frequencies present. It looks like a columns quite well defined ...
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1answer
44 views
How to calculate STFT of a function for a rectangular window
How to calculate the STFT (by hand) of $$u(n)\cos(0.2\pi n)$$ for a rectangular window of a length 20, positioned at $n = 5$.
I know that to use STFT I need to divide longer signal to a shorter parts ...
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1answer
66 views
Is possible reach the DFT if I have the DTFT?
My teacher told me that DFT is DTFT sampled, i.e.:
$$X[k] = X(e^{j \omega})\Bigg|_{\omega = \frac{2\pi k}{N}}$$
But, if I have the sine
$$ x[n] = \sin(\omega_0 n) $$
the DTFT is:
$$X(e^{j \...
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1answer
69 views
Figuring magnitude and phase response
I've got a linear time-invariant system $$y[n]=\frac{8}{9}y[n-1]+x[n]$$
which I transformed into a transfer function $$Y(z)=\frac{8}{9}Y(z)*z^{-1}+X(z) =>\frac{Y(z)}{X(z)}=\frac{1}{1-\frac{8}{9}*z^{...
