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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20 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
36 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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105 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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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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39 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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68 views

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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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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153 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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14 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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2answers
971 views

Finite and Infinite support in time and frequency domain

It's known that signals with a finite support in time has an infinite support in frequency (talking about Fourier Transforms). A common example that is given for the claim is the triangle function ...
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46 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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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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186 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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Comparison between Fourier transform, short time Fourier transform and wavelets

What is the difference between the Fourier transform, short time Fourier transform and wavelets?
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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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Compressive Sensing Incoherence Principle

As people acquainted with Compressive Sensing would know, incoherence and sparsity are two main principles. I've been reading about compressive sampling and developed an interest into the topic. What ...
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143 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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36 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
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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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48 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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2answers
497 views

Why phase information is usually ignored after Fourier transform?

Why phase information is usually ignored after Fourier transform? I have read in a tutorial [ref: FFT Tutorial] that interpretation of phase is usually challenging, so scientists do not show it or ...
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60 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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Intuition behind the scaling property of Fourier Transforms

The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally. On the ...
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2answers
1k views

Order analysis or order tracking

Last week I've been trying to implement the Order Analysis in MATLAB in vain. I've read a lot of docs about it like this one , but I still can't figure it out. This will be my last shot. Say I have ...
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131 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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134 views

From Fourier transform to Laplace Transform

It's well known that you can estimate the Fourier Transform $X(f)$ of a signal $x(t)$ via its Laplace Transform $X(s)$, just by setting $s = j2\pi f$ to the latter, as long as the region of ...
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797 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
36 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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2answers
1k 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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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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148 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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3answers
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Calculating an image's fourier spectrum by hand?

Suppose I have a $4x4$ image with the following values as its grey-level intensity for each pixel like this: I want to get its Fourier spectrum. Usually, I would just punch into Matlab and run a fft ...
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54 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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Fourier transform of a tilted line function

Assume a line function (line segment to ensure integration): $$y = a\cdot x + b$$ What is the Fourier transform of the line segment? Intuitively, it may give a sinc function, but actually not.
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499 views

Inverse Sliding DFT

From paper: Bradford R., Dobson R., ffitch J. - Sliding is Smoother than jumping In chapter 6 - Signal Reconstruction, the inverse of the sliding DFT can be achieved by this formula: $$f_0=\...
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Where is the flaw in this derivation of the DTFT of the unit step sequence $u[n]$?

This question is related to this other question of mine where I ask for derivations of the discrete-time Fourier transform (DTFT) of the unit step sequence $u[n]$. During my search for derivations I ...
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1answer
53 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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247 views

Simple $\sin(2\pi 1000t)$ Fourier transform in PSpice not behaving as expected

So I have this very basic circuit show below which I am simulating with PSpice. Now, when doing the Fourier transform of $\cos(2\omega1000t)$, I expect to see two impulses(one at -1kHz and one at ...
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1answer
197 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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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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2answers
84 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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1answer
47 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
19 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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222 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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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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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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90 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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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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26k views

Meaning of Real and Imaginary part of Fourier Transform of a signal

Say $f$ is a signal of time $t$, $F$ its Fourier transform of the variable $v$. It is known that in polar coordinate, $|F(v)|$ tells us how much the frequency $v$ is present over the signal, and $Arg(...