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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Z-Transform vs. Fourier Transform convergence
Are there signals for which the Fourier transform is known to exist (perhaps including
singularities) and for which the z-transform does not converge?
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2answers
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How to get Spectrogram after fft in matlab?
I have many EEG signals which record at 100 Hz. I use FFT on them with fft Matlab toolbox. Now I wanted to get a Spectrogram. As I searched and read a lot, I figure that I should window my signal and ...
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Calculating the Fourier transform of shifted scaled unit step function
I have $x_1(t)$ here. To get $x_2(t)$, I need to differentiate $x_1(t)$. Express $x_2(t)$ as $2u(t+2)-4u(t)+2u(t-2)$.
From Fourier transform definition integral, I got $X_2(j\omega)=\frac{2e^{j\omega ...
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1answer
54 views
Discrete and Continuous Signals
I am new to the signals area and have been reading through a lot and have some questions.
Suppose I have a saved audio file on my computer, .wav file. I can view the time domain of the signal by ...
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3answers
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Help with Audio Signal noise removing using FFT and IFFT in Matlab
I dont understand why my modified fft of a audio signal returns complex values after ifft.
I modified my signal by zeroing out all the unnecessary freq.
FFT: Fast fourier transfrom
IFFT: Inverse ...
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1answer
32 views
inverse fourier transform of magnitude and phase
I stuck this question. Frequency response is written as magnitude and phase and I don't find inverse fourier given signal which as magnitude and phase.How can I solve it ? Can you explain the solution ...
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1answer
29 views
Calculating the magnitude spectrum and phase spectrum
From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$.
Then, I want to calculate its magnitude spectrum and phase spectrum.
The ...
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2answers
76 views
Getting the DTFT from the DFT samples
How would you get the DTFT from the DFT samples?
How will the DFT indexes map to the discrete frequency and what kind of an interpolation would be required?
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2answers
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Help with finishing this integral, to obtain the power spectral density of a pure cosine wave
I am trying to evaluate the power spectral density $S_{xx}(f)$ of a cosine signal $x(t) = A\cos(2\pi f_0t)$, by starting from its definition for deterministic power signals
$$S_{xx}(f) = \lim_{T\...
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1answer
62 views
Visualizing the “frequency shift” theorem in FFT
I was trying to visualize the frequency shift theorem in MATLAB, which states that if the Fourier transform G(f) is shifted by a constant $f_o$, its inverse transform g(t) is multiplied by $e^{j2\pi ...
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1answer
54 views
Fourier Transform of sampled reflectance measurements
Goal:
Calculate the complex index of refraction ($\hat n = n +jk)$ from reflectance measurements.
Data:
Reflectance measurements for various materials were taken with a FTIR (Nicolet™ iS50 FTIR, ...
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5answers
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Inconsistency with the units of power spectral density and the definition the people often give
Perhaps someone can help me resolve something - this is my understanding:
In deterministic signal analysis, for a signal $x(t)$ the signal energy (as opposed to the real physical energy) is given by
$...
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1answer
34 views
Determine reflections from received signal
I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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1answer
31 views
How does a shift in time domain result in phase shift in frequency spectrum?
I am aware of the fact that a time shift of say $t_0$, results in a phase shift in the frequency spectrum. What confuses me is how this scales the rotational part of the transform by $t_0$ and doesn’t ...
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Division in the Fourier Domain (Deconvolution) - How to Handle Lengths of the Signals
In order to avoid circular convolution $y(t)$ of two functions say $u(t)$ and $v(t)$ in Fourier transforms, the data length must be at least ($u(t)$)+length($v(t)$)$-$1. If we are interested in ...
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2answers
103 views
Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain
My goal is to compute the Fourier of the product between two discrete time signals, y1 and y2. This can be done by computing the convolution between the fourier transform of y1, f1 and the fourier ...
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2answers
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Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD)
I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ...
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1answer
44 views
2D Fourier downsampling
How can one correctly downsample a Fourier 2D matrix of complex numbers ? More precisely, if I have a 2D DFT of an image:
x=phantom
X=fft2(x)
How should I do to ...
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1answer
49 views
Why is it assumed that $x[n]$ is limited from $0$ to $N-1$ while evaluating DFT?
I am a total beginner in this topic of DFT. I get that the series must be finite for DFT calculation. But everywhere we are assuming that this series must be limited from $0$ to $N-1$. How to evaluate ...
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1answer
51 views
What is the effect of padding zeros to FFT on time domain ? (opposite of what is usually done)
As above. I know that zero padding in time increasaes frequency resolution but I'm having a hard time to understand the opposite. How would you interpret that?
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1answer
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How do you find the phase of the DFT of a discrete signal?
My question is similar to this one and this one, but neither answers address my concern.
Suppose you have a signal x(n) = {-1,2,-3,2,-1} where we can assume x(0) = -3. So this is an even signal.
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1answer
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What is the relation between PCM amplitude values and the values in a Spectrogram?
I am curious to know the relation between the 16-bit amplitude values in the PCM-encoded signal and the values inside the corresponding spectrogram. I am using Scipy reading a 44100-sample rate song:
...
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2answers
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Is the Laplace transform a special case of Fourier transform? (Not the other way around)
Always had a thought about why Laplace transform reveals the transient properties of the system?
My doubt is based on the following fact,
Fourier transform is given as
\begin{equation}
\mathscr{F}\...
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2answers
47 views
Power Spectrum and Power Spectral Density
From signal theory we know that a very useful representation of some power signals is that of its power spectral density, whose curve represents how the total power of the signal is distributed at all ...
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0answers
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How to find phase of two fixed Gaussian of periodical signal (analytically)?
For a periodical signal define on $\phi \in [0, \pi * 2)$,
there was supposed to be two peaks,
may following Gaussian, but may also be Cauchy or other distribution with one peak,
plus Poisson noise.
...
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2answers
56 views
Best approach for discarding the ends of convolution in FT
In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. ...
2
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1answer
424 views
When to use Fourier, Laplace and Z transforms?
If we have an LTI system, with an input signal $x(t)$, impulse response $h(t)$ and output $y(t)$, I was under the assumption that if the input and impulse response were continuous in time, then you ...
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2answers
148 views
Linear and Circular Convolution in Fourier Domain (DFT)
Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
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1answer
89 views
Real-valued DTFT
Now this is a simple question, but I still ask it for clarification:
I know that an even signal $$h[n] = h[-n]$$ results in a real-valued DTFT (we have proven that in class). Now my question is the ...
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1answer
54 views
Assume frequency response of x(t) is X(f). Find frequency response of x(-2t+4)?
Frequency response of $x(t)$ is $X(f)$. Find frequency response of $x(-2t+4)?$
Here is my work using the fourier transform property:$
x(-2t+4) = x( -2(t-2) )$,
+ First, I apply the property, $x(at)$ ...
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Are higher frequency components of constant amplitude of a square wave dependent only on the rise time and independent of square wave frequency?
This question based on the observation that ringing on square wave due to multiple reflections on a transmission line doesn't change with the change in frequency of square wave.
From this observation ...
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1answer
33 views
How to simplify multiple addition and convolution operations into one convolution kernel
I need to perform such a conversion to simplify my image processing problem (sharpening, in green are the knowns, in red the unknowns):
\begin{align}
y(n,m) &= \color{green}{x(n,m)} * \left[ \...
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1answer
60 views
How to understand the sum of all “fourier frequencies”?
I got the data of an acceleration sensor to analyze. It consists of special terms of 30 Hz, 60 Hz and 120 Hz. In the following you can see in the first plot the 60 Hz data and in the second one the ...
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1answer
121 views
Evaluating the continuous Fourier transform of a constant, and matching it up with the FFT result
I am following my optics textbook (Optics, by Eugene Hecht), throughout which are given various exact analytical results for the diffraction patterns that result from light passing through differently ...
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Create 2-d Dirichlet kernel for use in image processing
I am working on frequency domain CNNs for image classification task, in which I initialize complex kernels of size (k*k). For performing point-wise multiplication between the kernel and the Fourier ...
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1answer
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Quadrature signal acquisition simulation
Bottom-line: how to create a 90 degrees out of phase signal from the real part of the fourier transform of a 1D signal (i.e., fft of a line of an image). ? *(I *(I think the Fourier shift thm can help ...
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1answer
63 views
How to make low pass filter using frequency sampling method?
https://www.allaboutcircuits.com/technical-articles/design-of-fir-filters-using-frequency-sampling-method/
So there is two main equation:
I wish to filter out frequency $\le 10000Hz$, for example. ...
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1answer
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1answer
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How to do the Fourier Transform of bounded function?
I was trying to solve a Fourier transform of a function using the properties of Fourier transforms. The function is given as:
$\frac{At}{2}$ for $-2<t<2$ and $0$ for all other $t$. Doing the ...
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2answers
58 views
Window functions and the Fourier transform
I want to clarify the 'correct' way to use windowing and Fourier transforms.
My question is somewhat related to this one, but I have a few additional queries.
I have some real, non periodic signal ...
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2answers
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Why am I not getting a flat phase for a Gaussian pulse when doing a Fourier transform in Python?
I have been trying to obtain a spectrum and a spectral phase of a Gaussian pulse using the Fast Fourier Transform provided with numpy library in Python. Here are ...
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Linearity of Fourier Transform [closed]
Given the CTFT pair above, I am trying to find a Fourier transform of
I thought I could multiply both sides(time domain and frequency domain) by to get the CTFT pair in the following form:
But that ...
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1answer
45 views
Torque signal fft
I have the following torque signal picked up with a 10.240Hz sampling rate from a testbench.
I am studying its fft which I create on Octave with the following code:
...
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1answer
61 views
A Delay Between Two Filtered Chaotic Signals
it is a common practice to use a shift of cross-correlation peak to evaluate a group time delay of two signals (chaotic signals are included). Can one synchronously and equally filter these chaotic ...
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average value of modulated signal with Fourier Analysis
I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
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1answer
58 views
Subtract background from 2D signal using spectral methods
I have a 2D signal, with intensity as a function of two angles (alpha and beta), as shown below.
This contains a background, which makes the signal's base-surface locally convex-concave. I would like ...
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Why does spectral accuracy of laplacian decrease with sampling size?
We know that for any real-valued function $f(x,y,z)$ whose Fourier transform is $\mathcal F[f]$, its laplacian can be computed from a spectral interpolant as follows.
$$
\Delta f(x,y,z) \simeq \sum_{...
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How to create a synthetic time series where power spectral density estimation is achieves better results than a direct Fourier transform?
I am trying to create a synthetic time series where PSD estimation is necessary and useful to recover the correct spectral information of the time series. But so far I can only create a time series ...
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2answers
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Inverse Fourier transform Of a triangular impulse
I have to find the expression of this graphic and after find the inverse Fourier transform of it. First of all I found that the expression of the graphic is $$ X(f) = \frac{1}{2} tri (\frac{f+f_0}{B}) ...
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1answer
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Discrete Fourier transform - Norms of complex input signals and their transformation
Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold?
The question is given to me like this with ...
