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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Basic difference between Fourier transform and laplace transform?
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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29 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 $t=0$:
$$F(j\...
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1answer
55 views
2-d circularly symmetric low-pass filter
For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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confusion about output of inverse fourier command in MATLAB?
I am reading book of alex palamides chapter 6 fourier transform
and i am trying to compute inverse transform of a function but when i write the code of book in MATLAB,i do not get expected answer(as ...
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31 views
Applicability of Fourier transform to periodic signals? [duplicate]
Can we use Fourier Transform for periodic signals or only we can use fourier series with periodic signals?
I am asking this question because I read on page 301 of alex palamides as shown highlighted ...
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69 views
Difference between CTFT and DTFT?
I have tried to read different articles but still confused in difference between continuous time Fourier transform and discrete time Fourier transform?
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61 views
Division of sines as sinc
$\DeclareMathOperator\sinc{sinc}$I've come across a text that states that $\frac{\sin(\frac{3\pi}{10}n)}{\sin(\frac{\pi}{10}n)}, n=0\ldots9$ is a 'weighted' $\sinc$ function. Thus, its Fourier ...
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1answer
27 views
Inverse Fourier of Two-Pole Transfer Function
I would appreciate if someone could walk me through this derivation.
I have a transfer function in the frequency domain, which has two poles
$$\tilde{H}(\omega) = \Big(\frac{1}{1 + i \omega \tau_1}\...
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Filtering Step Function in Frequency Domain
I have a step function, and I perform Forward fourier transform on it. As result of this transformation, I obtain a frequency domain representation in this picture: https://www.researchgate.net/figure/...
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1answer
60 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
123 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:
$$H(z)=\frac{(1-0.5z^{-1})(1+4z^{-2})}{(1-0....
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Intuitive understanding of Fourier transform of images [duplicate]
I am trying to have an intuition about the Fourier transform of images
For example the image on the right is the Fourier transform of the image on the left,
my question is :
1)Why are the ...
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1answer
41 views
Why am I not getting the intended coefficients in this 2D Fourier demonstration?
I am trying to demonstrate how the 2D Fourier decomposition of an image works with Matlab and a very, very simple example.
I create a 4 x 4 pixel image with cosine basis vectors as such:
...
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1answer
35 views
What is the type number of a discrete time system given $H(z)$?
Given a continuous time impulse response $h(t)$, if I take the Laplace transform and count the no. of poles at origin, that gives the type number of the system. For e.g., $$H(s) = \frac{2}{s(s+2)}$$ ...
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Overlapping in real time fourier transform?
I have an algorithm and I need to record audio and perform short time Fourier transform to obtain which frequency is the most common. I am using a Hanning window to try and reduce spectral leakage as ...
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2answers
57 views
What is the interpretation of Fourier Transform containing only imaginary part?
The FT of a unit step function is taken as:
$$
X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}
$$
The transform only has the ...
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Why is the ROC of Laplace transform independent of imaginary part of s?
An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise.
Now sticking to the mathematical notation of Laplace transform, ...
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1answer
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Fourier Transform of the Hilbert Transform of cos(t) (using Fourier time-shifting property)
If $x(t)=cos(t)=\frac{1}{2}e^{jt}+\frac{1}{2}e^{-jt}$, then $X(\omega)=\pi \delta(\omega-1)+\pi \delta(\omega+1)$. If $y(t)=cos(t-\frac{\pi}{2})=\frac{1}{2}e^{j(t-\frac{\pi}{2})}+\frac{1}{2}e^{-j(t-\...
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Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?
Let
$$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$
Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure
what will the frequency domain for $Y(\nu)$ look like for a ...
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1answer
40 views
Matlab FFT not producing symmetric spectrum
I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset.
...
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1answer
46 views
What is the physical interpretation of the absolute value of a fourier transformed signal, $\left| F(t)\right|$?
If one has some oscillating voltage signal, for example:
$$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
60 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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23 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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50 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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1answer
34 views
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
39 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
120 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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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
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“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
61 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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1answer
71 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/...
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How to get descrete fourier tarnsfom [closed]
Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
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1answer
47 views
Reconstructing a signal from FFT by adding individual signal components
I'm attempting to reconstruct a signal from the DFT of the signal. I tried to do it by extracting the individual sinusoids and adding them up, but the answer I get is incorrect.
...
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1answer
68 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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2answers
97 views
Fourier Transform of Alternating Periodic Rectangular Pulse
I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem.
Given the signal is periodic I could use formula for Fourier transform of periodic signals:
$$...
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1answer
51 views
Applying frequency-domain filters on a centered Fourier transform
I understand why we shift the Fourier transform such that the 0-frequency is centered for visualization. In the shifted DFT(u,v) of an M*N 2-dimensional image,
the top-left corner of the 4th quadrant ...
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0answers
40 views
Finding the input from the impulse response and output
I have $y,h,x$ which are all vectors.
From $y[n]=x[n]*h[n]$ which is basically how I got $y[n]$. I also know $h[n]$.
I put this through a Fourier transform. Let's assume that the capitalized ...
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2answers
54 views
What should my reference value be when converting FFT bin amplitudes to dB?
I want to transform my FFT output values into a dB scale, but I'm struggling to determine the function I should run each bin amplitude through. My understanding of the decibel scale is that a value ...
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1answer
52 views
Discrete Time Fourier Analysis
Suppose we're given the following:
$ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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1answer
40 views
Plotting the Phase Response
I would appreciate it very much if someone would be able to provide some clarity on plotting phase responses.
For instance, given that the frequency response of a filter can be written as H(exp(j*&...
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1answer
34 views
Fourier Transforms, symmetry, real/imaginary
I was hoping to clarify if the following was correct:
-a real function (neither even nor odd) in time exhibits conjugate symmetry in frequency, so the real part of the frequency response is even, and ...
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29 views
How would I find the function given the magnitude plot and the phase response?
I'm wondering how I'd find the Fourier Transform X(jw) given the following information:
My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
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2answers
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Significance of modular arithmetic in DFT?
In what ways does modular arithmetic plays a part in DFT?
Why is it a so integral part of DFT?
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1answer
50 views
Inverse Fourier Transform From Plots (2019 edition) [closed]
Hello I borrowed the title for another post.
I cannot figure out how to find the inverse fourier transform from this spectrum.
I know what the transform is
I'm sorry for the plot being hard to ...
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29 views
Low pass filter transfer function
I am calculating the transfer function of a low pass RC filter and I have gotten $\frac{1}{1+jωRC}$ which is correct. But somehow it seems $ωRC = \frac {ω}{ω_0}$ that refers to the cutoff freqency ...
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1answer
40 views
Help me understand the stages involved in filtering a signal using Discrete Fourier Transform
I have a series of discrete values measured from a sensor. I want to filter the frequencies coming from this sequence of values. Then, if I understood the process correctly this is what I do:
I ...
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1answer
65 views
Extrapolate a 2D array using Fourier Transform
I need to extrapolate a given 2D array to a larger domain, keeping the spatial frequency. This is the original field:
(the data file in numpy npz format and a Jupyter notebook to plot it can be found ...
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The Fourier Transform of a periodic function and it's series
Let $X(f)$ be the Fourier transform of $x(t)$:
$$ X(f) \triangleq \mathscr{F}\Big\{ x(t) \Big\} = \int\limits_{-\infty}^{\infty} x(t)\,e^{-j 2 \pi f t} \ \mathrm{d}t $$
$$ x(t) \triangleq \mathscr{F}...
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1answer
99 views
Normalized cross-correlation in frequency domain
I never worked with signal processing and never really used Fourier transforms before, still I am working on a project consisting on taking the output of an accelerometer to detect some movement ...
