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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Fourier transforms and time shift
There is probably something trivial behind this, but I am missing something. I need to create a stationary random time series data v(t) which is the the sum of another time series u(t) and u(t) with a ...
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16 views
Detecting changes in signal due to server delay
I'm currently working on an application that can be used to determine when a signal changes due to a server delay. Essentially, I have an API that is used to output data to a UI. However, for reasons ...
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1answer
30 views
Reconstructed output mismatch for LTI system
I have a system with measured input (u) and output (y).
I assume that this is an linear time-invariant (LTI) system and I want ...
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2answers
43 views
Image Brightness on 2D Fourier Transformation
What effect does the brightness have on the frequency spectrum of 2D Fourier Transformation?
Example. Suppose we have a gray image and calculate 2D Fourier Transformation. Then we increase the ...
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4 views
What's the significance of lomb-scargle power?
What is the significance of Lomb-scargle power (y-axis)?
I have two data sets. For each plot, above plot is Lomb-scargle periodogram of the lower plot (original data).
The first data set has an ...
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1answer
20 views
Nyquist Frequency on semi-unevenly sampled data
I have a data set that has 'kind of' constant sampling rate - it switches between 1 min and 2 min. About 70% of the times, samples are taken every 1 minute, and about 30%, samples are taken every 2 ...
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42 views
Unit of Energy Spectral Density
The continuous-time Fourier Transform (CTFT) of a signal $x(t)$ (with unit $unit$) is:
$$X(\omega)=\int_{-\infty}^{\infty} x(t)e^{-i\omega t}dt$$
which should be in $unit\cdot sec$ or $\frac{unit}{...
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Phase response of $H(f)=e^{-j2{\pi}ft_0}$
Given is the impulse response: $$h(t)=\delta(t-t_0)$$.
I calculated $$H(f)=e^{-j2 \pi ft_0}=|H(f)|\cdot e^{j\varphi(f)}$$.
Now, the magnitude response of $H(f)$ is:
$$\begin{align}
|H(f)| &=\...
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47 views
Python FFT outptut
I have a (real) array of data and am trying to analyze its frequency components. I've been using NumPy's FFT routines, but I realized there is something I don't quite understand: why does the output ...
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47 views
How to normalize PSD to get the same magnitude as FFT peak
I am trying to use FFT and power spectra density estimation with python (np.fft.fftand scipy.signal.periodogram). And trying to ...
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8 views
Symmetry in Lomb-Scargle transformation
I'm observing weird symmetry and repeating pattern on my unevenly sampled time series data after Lomb-Scargle transformation. I used astropy lomb-scargle.
...
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23 views
Correlation/anticorrelation as a function of frequency
I am tracking the values of two fluctuating quantities as a function of time and am trying to analyze possible correlations between the two as a function of frequency. The application is experimental ...
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34 views
Effect of Nyquist frequency on Fourier transformed data
Upper plot is the original data's plot, and the bottom plot is Fourier transformed data. For the bottom plot, x-axis is the frequency and y-axis is the amplitude. I don't understand the weird behavior ...
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1answer
37 views
fftshift in MATLAB with even number of data points in double sided spectrum
I have a question with reference to this Table.
With even N, the frequency axis extremes should be $\pm$Fs/2, where Fs is the sampling frequency. However in the array we have only one value ...
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1answer
57 views
Frequency Axis of Discrete Fourier Transform (DFT) with Odd Number of Data Points
I am trying to understand the logic behind making a frequency axis in DFT. I am using for time based light absorbance. When we have even number of data points (N= even integer), collected over a ...
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1answer
35 views
Fourier Transform within a certain Limit
I want to evaluate fourier transform within a certain limit in MATLAB,the expression of which is
$$X(f) = \int_{1}^{4}{x(t)e^{-i2\pi ft}}\,dt$$
I have to find value of the above expression ...
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1answer
27 views
Is there any way that we can perform speech recognition without using Fourier transforms?
I am trying to research about speech recognition and why everyone uses Fourier transforms in going about the topic. I know that we get information related to the frequency of each sound uttered which ...
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32 views
Is there a generalized method to get the input with the given output and the impulse response?
$y(t)=y(t+12), y(t) = x(t) \ast h(t)$
The continuous time signal output $y(t)$ is a periodic square wave, 50% duty cycle pulse.
The impulse response is a box function.($A = 1, T = 2$)
By using ...
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1answer
39 views
inverse discrete fourier transfor with plain python
I am trying to calculate inverse discrete fourier transform for an array of signals.
I am using the following formula:
And my python code looks as follow.
...
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24 views
What is the intuition of convolution theorem [duplicate]
As the question suggest, can anyone explain intuitively why the convolution theorem works ?
For convolution theorem, I refer to convolution theorem from Wikipedia
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31 views
Plot Frequency Spectrum of Binary Sequence in Matlab
I am new to Matlab and I am trying to implement a section of a published paper, the basic idea of the part that i am implementing is to show the frequency spectrum of camera aperture. The shutter ...
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1answer
76 views
Basic difference between Fourier transform and laplace transform? [duplicate]
I have read few links about difference between Fourier transform and Laplace transform but still not satisfied
Please correct me if i am wrong
Simply put, the main difference between Fourier ...
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1answer
34 views
Why does subbing $s = j\omega$ into the Laplace transform of a cosine wave yield a purely imaginary result?
The Laplace transform of a cosine starting at $t=0$ is given by
$$F(s) = \frac{s}{s^2 + \omega_0^2}$$
If I sub in $s = j\omega$, I get the Fourier transform of a cosine starting at $t=0$:
$$F(j\...
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1answer
112 views
2-d circularly symmetric low-pass filter
For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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32 views
Applicability of Fourier transform to periodic signals? [duplicate]
Can we use Fourier Transform for periodic signals or only we can use fourier series with periodic signals?
I am asking this question because I read on page 301 of alex palamides as shown highlighted ...
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153 views
Difference between CTFT and DTFT?
I have tried to read different articles but still confused in difference between continuous time Fourier transform and discrete time Fourier transform?
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37 views
Inverse Fourier of Two-Pole Transfer Function
I would appreciate if someone could walk me through this derivation.
I have a transfer function in the frequency domain, which has two poles
$$\tilde{H}(\omega) = \Big(\frac{1}{1 + i \omega \tau_1}\...
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1answer
64 views
Output of an LTI system given its transfer function and input
Given the transfer function $$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$ and the input $$v_i(t) = 0.1 \sin(100t)$$ find the output, $v_o(t)$.
My approach was to use $v_o(t) = \mathcal{L^{-1}}\left\{T(...
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1answer
136 views
Cepstrum Calculation of Rational Function H(z)
I am trying to solve my first problems at cepstrum calculation. I want to calculate the complex cepstrum $\hat{h}[n]$ of a signal $h[n]$ with Z-Transform:
$$H(z)=\frac{(1-0.5z^{-1})(1+4z^{-2})}{(1-0....
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26 views
Intuitive understanding of Fourier transform of images [duplicate]
I am trying to have an intuition about the Fourier transform of images
For example the image on the right is the Fourier transform of the image on the left,
my question is :
1)Why are the ...
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1answer
52 views
Why am I not getting the intended coefficients in this 2D Fourier demonstration?
I am trying to demonstrate how the 2D Fourier decomposition of an image works with Matlab and a very, very simple example.
I create a 4 x 4 pixel image with cosine basis vectors as such:
...
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37 views
What is the type number of a discrete time system given $H(z)$?
Given a continuous time impulse response $h(t)$, if I take the Laplace transform and count the no. of poles at origin, that gives the type number of the system. For e.g., $$H(s) = \frac{2}{s(s+2)}$$ ...
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2answers
46 views
Overlapping in real time fourier transform?
I have an algorithm and I need to record audio and perform short time Fourier transform to obtain which frequency is the most common. I am using a Hanning window to try and reduce spectral leakage as ...
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2answers
66 views
What is the interpretation of Fourier Transform containing only imaginary part?
The FT of a unit step function is taken as:
$$
X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}
$$
The transform only has the ...
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33 views
Why is the ROC of Laplace transform independent of imaginary part of s?
An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise.
Now sticking to the mathematical notation of Laplace transform, ...
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1answer
13 views
Fourier Transform of the Hilbert Transform of cos(t) (using Fourier time-shifting property)
If $x(t)=cos(t)=\frac{1}{2}e^{jt}+\frac{1}{2}e^{-jt}$, then $X(\omega)=\pi \delta(\omega-1)+\pi \delta(\omega+1)$. If $y(t)=cos(t-\frac{\pi}{2})=\frac{1}{2}e^{j(t-\frac{\pi}{2})}+\frac{1}{2}e^{-j(t-\...
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Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?
Let
$$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$
Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure
what will the frequency domain for $Y(\nu)$ look like for a ...
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1answer
45 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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1answer
57 views
What is the physical interpretation of the absolute value of a fourier transformed signal, $\left| F(t)\right|$?
If one has some oscillating voltage signal, for example:
$$V(t) = V_{max}\cos(2 \pi \nu_{0}t) e^{-\gamma t}$$
and you take the Fourier transform of this in the usual way to get:
$$\hat{V}(\nu) = V_{...
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31 views
Fourier transform pair for $ln(ln(…))$ cascade?
I need to analyze real signals $y_i$ in the frequency domain. $y_i$ are defined like:
$y_1 = ln(ln(x))$
$y_2 = ln(ln(ln(x)))$
$y_3 =~ ...$
$...$
Are there Fourier transformation pairs for this ...
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1answer
64 views
Why do the two methods give different answers for the Fourier transform of $Y = \cos(\omega_0 t + \phi)$?
Why do the following two methods give different answers (or are they the same) for the Fourier transform of $Y = \cos(\omega_0 t + \phi)$, with respect to $t \to \omega$ ?
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24 views
Using MATLAB to plot the input and the magnitude spectrum of the signal
I have an aperiodic signal $v_{out} = e^{-t} u(t)$ (real exponential signal) from discharging capacitor.
I was trying to plot using MATLAB 15 seconds of this signal in time domain? I am thinking how ...
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55 views
How is the decay of a signal exemplified in a Fourier Transform?
Is there any way to tell if a signal is decaying from its fourier transform?
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What is a periodic signal in image processing?
In the context of image processing (and computer vision), the concept of convolution comes up a lot. Convolution is quite related to the concept of Fourier transform and DFT. In the context of image ...
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1answer
42 views
DTFT frequency range
$$X(e^{j\omega}) = \sum_{n=-\infty}^\infty x[n] e^{-j\omega n} $$
The frequency term $\omega$ in DTFT is normalized as $\omega = \frac{\Omega}{f_\mathrm{s}}$
$\Omega= 2 \pi f$ is the angular ...
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3answers
172 views
How Much Zero Padding Do We Need to Perform Filtering in the Fourier Domain?
Consider an $M\times N$ image $f$ and an $G \times K$ filter $h$. Given that convolution in the spatial domain corresponds to multiplication in the Fourier domain, then we can perform a convolution of ...
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1answer
41 views
Applying duality property to fourier transform of unit step function
For Continuous time aperiodic signals, the duality property of Continuous Time Fourier Transform (CTFT) is following
$$\mathscr{F}\Big\{x(t)\Big\} = X(f), \qquad\text{then} \quad \mathscr{F}\Big\{X(t)...
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3answers
62 views
“Dirac Comb” vs “Ones Comb”
While learning sampling theory - I noticed that examples of continuous signal sampling always achieved the goal via multiplying the signal with a "Dirac Comb".
I was intrigued by the requirement to ...
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2answers
64 views
Ideal sampling using sinc funcion
Let $ x(t) $ be a bandwidth limited signal such as $ \forall |\omega|>\frac{\pi}{T} : X^F(\omega)=0 $ while $ X^F(\omega)$ is the signal's Fourier Transform.
Let us denote $y[n]=\int_{-\infty}^{\...
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101 views
Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?
I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts:
https://www.researchgate.net/post/...
