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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Can largest-triangle-three-buckets downsampling method used with fourier transformed signal?
I've been reading on the largest-triangle-three-buckets downsampling method for downsampling. Though it was originally published in the thesis "Downsampling Time Series for
Visual Representation&...
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21 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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Reconstruct $x(t)$ from $y(t)$ and $z(t)$
Let $x(t)$ be band-limited signal with $X(j\omega) = 0$ for $|\omega|\gt \omega_M$. We use $$s(t) = \sum_{k =-\infty}^{+\infty}(-1)^k\delta(t - \frac{kT}{2})$$ for sampling. So we have $z(t) = x(t)s(t)...
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Fourier transform of the sampled signal
I want to calculate Fourier transform of the sampled signal in two ways. Let $$s(t) = \sum_{k = -\infty}^{\infty}\delta(t - kT)$$And $z(t) = x(t)s(t)$. So we have $$z(t) = \sum_{k = -\infty}^{\infty}x(...
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34 views
Getting the power of a signal from its Fourier transform?
I have a non-periodic signal that contains the sinc function in the time domain and so it is a bit difficult to calculate its power (because of the integral) through:
$$ {P_x} = \lim_{T \to \infty} \...
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1answer
36 views
Frequency Domain Distribution
I have a complex signal in the time domain normally distributed. What will be its distribution in the frequency domain?
I assumed since the frequency domain is a linear transformation the distribution ...
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2answers
34 views
Does Short-time Fourier transform impact quality of signal?
I am playing with spleeter to separate voice from an audio signal.
They go to the frequency domain by computing the Short-time Fourier transform to create a spectrogram. As there are some ...
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34 views
Meaning of negative frequencies in Baseband non sinusoidal, non periodic signal
I can understand the meaning of negative frequencies in a sine or cosine signal, since by using Euler's identities, you have two complex phasors moving to different directions, which when added, give ...
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1answer
170 views
Fourier transform of the magnitude of the fourier transformed signal
I've come to realize that the Fourier transform of an already Fourier transformed signal gives the time-reversal signal.
$$\mathcal F(\mathcal F(x(t)))=x(āt)$$
ref 1,ref 2
However, my question is, if ...
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1answer
37 views
Behaviour of integrator at steady state
I wanted to calculate response of integrator of sinusoidal input at steady state via these two methods as mention in image but these two methods give two different answers at steady state, so where ...
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23 views
RMS of signal vs average amplitude
I am trying to estimate the average amplitude of some signal with frequency 6 Hz, sampled at ~300 Hz. See figures for a part of the signal and its dft calculated using matlab.
I estimate the average ...
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37 views
Frequencies of complex exponentials in Discrete Fourier Transform
What I understand is that using DFT, we are representing a given discrete signal using a basis of complex exponentials of different harmonic frequencies. If I am taking 16 point DFT of a signal ...
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MRI K-space to image: why track frequencies in two dimensions?
While trying to better understand how an MRI goes from k-space to an image, I came across this wonderful website that explains how you would represent an image as a collection of rows of pixels where ...
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1answer
25 views
Names of system functions in frequency domain
I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these functions ...
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2answers
62 views
Showing error energy goes to zero
Let
$$\hat{x}[k] = \frac{1}{2\pi}\int_{-W}^{W}X(e^{j\omega})e^{j\omega k}d\omega,\label{ift}\tag1$$
where
$$X(e^{j\omega}) = \sum_{n=-\infty}^{+\infty} x[n]e^{-j\omega n}\label{dft}\tag2$$
Also,
$$d[k]...
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45 views
Steady state variance of a stochastic differential equation - relation between the frequency and time domains
Consider a stochastic differential equation:
$$
dx(t) = a x(t)dt + b y(t)dt \quad (1)
$$
where $y(t)$ is a stochastic process satisfying $\langle y(t)y(t')\rangle = \delta(t-t')$. We will assume that ...
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1answer
32 views
Conjugate symmetry of the DFT of real-valued sequences
I have read about Fourier transformation that real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. For ...
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29 views
Understanding index transformation in derivation of Fourier transform for sampling rate reduction
Was going over some notes regarding deriving fourier transform equation for Sampling Rate Reduction. Reference to Notes from below link https://ocw.mit.edu/courses/electrical-engineering-and-computer-...
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1answer
78 views
Auto Tune Shifting
So i have an algorithm that gets the fundamental frequency of windows, and can shift the pitch of each window as well (by a factor of x). For example. if x is 2 and the f0 is 440, the resulting f0 ...
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1answer
20 views
Spectral analysis of a cross correlation function [duplicate]
So it's widely known that the Cross Correlation of 2 signals helps us in figuring out the time delay in those signals by analyzing the peak of the correlation coefficient in the time domain.
For ...
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1answer
44 views
Fourier transform of an integrator filter
I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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Does it make sense to apply convolution in the frequency dimension of a fourier transformed signal?
What I have is more likely a theoretical question. Since I am not from a signal processing background it is hard for me to grasp the issue in using convolution in the frequency dimension of a Fourier ...
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2answers
75 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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34 views
What is the gradient of fft?
I have a time-series of length N generated by the following equation:
...
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1answer
24 views
Fourier Transform of a PSD and response of a PSD input
Does a Fourier Transform of a white noise exist?
If so, what is its general form?
It is possible to compute the fourier transform of a Power Spectral Density?
My problem in detail. I have to compute ...
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2answers
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How to interpret the window size and FFT size while performing FFT? [closed]
I have a discrete signal of length 98,000 samples and I am supposed to a FFT of the discrete signal with certain window size and FFT size. Can someone help me explain what is meant by the window and ...
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2answers
62 views
Proof of fourier transformation of multiplication of two signals
I've been trying to find a proof of the following, but still I m unable to proof it, can someone help me?
$$
ā±[x(t)g(t)] = \frac{1}{2\pi}
[X(\omega)*G(\omega)]
$$
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2answers
45 views
Understanding zero-phase filters
I'm reading the book "Digital Image Processing" by Gonzalez and Woods and I'm wondering how their definition of zero-phase-shift filter is equivalent to the one given here.
"Digital Image Processing" ...
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1answer
84 views
DFT symmetry vs DFT duality in Richard Lyons' “Understanding DSP”
I am reading Richard lyons, understanding dsp, chap 3.
Article 3.2 is about property of dft symmetry but any where in this chapter, i am unable to find discussion about dft duality property
I want ...
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81 views
Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$
Let
$$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$
Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$?
If not, what's the reason for ...
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33 views
Zero-padding or Interpolation in 3D FFT
I'm trying to perform a FFT of a 3D regular grid and then compute the bin average (in spherical shell bins) of the Fourier transformed grid.
The problem is that the resulted vector is very noisy as I'...
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Calculating Transfer function numerator and denominator from the rationalfit model
I have a frequency response data called 'AC_data' which is a vector of complex numbers (real and imaginary part) at different frequency points.
I have calculated a rationalfit model for the AC_data ...
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56 views
Wavelets vs Fourier Transforms
It's supposed that computing a spectrogram for a signal is faster using wavelets. However, wavelets need to be applied to the signal for every time step and frequency, giving the implementation a time ...
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2answers
75 views
Impulse response of a time scaling system
Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system?
\begin{array}{l}
X( \omega ) \ =\ \int ^{\infty }_{-\...
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What is the DFT of a binomial filter?
I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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1answer
48 views
Fourier transform of unit step
I was reading pdf by caltech and in one of its section, Fourier transform of Unit step signal is calculated but I am confused, how this can be possible if region of convergence for Laplace transform ($...
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2answers
84 views
Why can we have non-integer frequency bins in FFT?
I am studying DFT/FFT and I'm very confused about one thing. I read online that the frequencies we can sample with DFT must be integer (Why does the frequency in the DFT have to be an integer?). Later ...
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1answer
68 views
Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I donāt know how ...
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finding FL and FH from continuous time signal
I have a continuous signal $x_{a}$ which is defined as $X_{a}(F)=0$ for $|F|>B$.
Now if I multiplied the continuous signal $x_{a}$ by $cos6\pi Bt$. Then the fourier transform of the signal can be ...
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1answer
38 views
Confusion regarding DFT calculation?
I am studying Richard lyon chap3
, article "Understanding the DFT equation "
But i am bit confused how x(n) is calculated specially x(0) and x(1) because apparently x(n) is calculated by plugging ...
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1answer
56 views
Pitch shifting with bins creating large feedback
I am attempting to create a pitch correction algorithm. I started by performing a test. The test goes as such:
Get WAV file
Split it into bins of size n (512 in my case)
Shift each bin by 2 semitones ...
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0answers
19 views
How to identify the frequencies of periodic peak signals in a noisy time series?
Suppose to have two time series with peak signals at different frequencies, like these two:
...
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1answer
34 views
Construct IFFT from only the major frequencies of an input signal?
I have data which when plotted looks like the green line in the below image. The data is from the walking-motion of a reinforcement-learning-model in a simulation and therefore the values do not ...
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2answers
44 views
DFT without knowing the exact value of sampling rate?
I have a sequence of (real) numbers that represent the magnitude of a certain natural event. I know that the samples are equispaced in time, but not the exact value of the spacings. So does that mean ...
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5answers
100 views
Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?
When I look for the cause of the mirroring of frequencies in DFT output, I get two types of explanations:
The first one which says the frequencies are mirrored because of the complex exponential ...
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1answer
29 views
Cepstrum of white gaussian noise
What are the statistics of the cepstrum of gaussian white noise?
\begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT}
x_i &\sim \...
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64 point FFT Hamming window interpolated to 720-point sequences
Can someone here explain the meaning of, 64 point FFT Hamming window interpolated to 720-point sequences and its inverse?
720 point is from 0 to $2 \pi$ or (0 to 720 degree). I get the 64 point ...
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1answer
49 views
GSP as an extenstion of DSP
I am a PhD. in pure mathematics.
Could you please illustrate the following statement: the eigenvectors of a graph Laplacian behave similarly to a Fourier basis, motivating the development of graph-...
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27 views
GSP as an extenstion of DSP
I am a PhD. in pure mathematics.
Could you please illustrate the following statement: the eigenvectors of a graph Laplacian behave similarly to a Fourier basis, motivating the development of graph-...
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0answers
59 views
Is rotation of a Fourier transform the same thing as Fourier transform of a rotation?
I'm working on an image processing problem and wondering if DFT(rotation(image)) == rotation(DFT(image)) (1). My final goal is to apply rotations in the Fourier domain then do an inverse Fourier ...
