Questions tagged [transform]
In signal processing, a transform is a mathematical technique to convert data in one domain to another. The most common example is using the Fourier Transform to convert data from the time domain to the frequency domain.
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Proof that there cannot be two non overlapping ROCs for LTI system Laplace Transformation [closed]
Given an LTI system where the X(S) s-plane looks like this:
------O-----------O------O-------O---------
P1 P2 P3 P4
(the os represent poles ...
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How to avoid the edge effects that may occur when applying the Hilbert transform (by mirroring)?
How to avoid the edge effects that may occur when applying the Hilbert transform (by mirroring) for image or image series signal?
Code is appreciated (in python) please.
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What's the meaning of the amount of frequency 0 in the Fourier Transform?
In the Fourier series, I knew that the coefficient $a_0$ represents the DC value, shifting the signal up and down by the amount.
Then, what's the actual meaning of the amount of frequency $0$ in the ...
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Why DCT-III is not used as forward transform for image compression applications?
DCT-II is the most widely used type for image compression. This is due to its "Energy Compaction" property. According to this property, a good enough reconstruction of a natural image can be ...
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Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?
Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
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Calculating transform for maximum decorrelation?
Suppose you have a set of $n$ sensors with overlapping sensitivities--like the cone cells of an animal retina, which is in fact the sort of system I am trying to model. Given the frequency-response ...
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What are the modes of a transform basis?
So, I'm reading Steven Brunton's book, "Data Driven Science & Engineering", and I'm trying to understand what he means by mode in this following excerpt:
Most natural signals, such as ...
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Real and imaginary parts of the Fourier transform of a pure cosine wave
My understanding of the Fourier transform is that the FT of a cosine wave should be non-zero in the real part and all zero in the imaginary part. This follows from the orthogonality of sine and cosine:...
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Representation of Sampling Frequency in the Fast Fourier transform
I have 21600 data in the time domain. What Sampling frequency should I use? can someone explain the effect of showing the result by selecting different sapling frequencies?
Cheers
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Implement a simple Continuous Wavelet Transform for specifics frequency
I have a question. I am worked with the Wavelet Transform, Continuous and Discrete. With the Discrete Wavelet I implemented a noise reduction in a signal, using Python library.
Now i have a signal ...
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An new arranging of the discrete Sine transforms
Let $n$ be even and consider the non-normalized discrete Sine transform of type 5 which is
$$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$
Let us denote $s_{-,l}$ by the $l^{th}$...
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sampled FT of Continuous time LTI output
I am trying to compute the sampled Fourier Transform of a Continuous Time LTI system output. $x(t)$ is the input of LTI and $h(t)$ is the impulse res. $y(t)$ is the output. we know that
$$ y(t) = \...
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Effect of overlapping percentage on STFT output
I know STFT is generally applied to non-stationary signals but I tried to apply it to a stationary signal to get a working knowledge.
I created a stationary signal composed of three frequencies as ...
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Calculating signal power from Continuous Wavelet Transform in MATLAB
I would like to ask a question about the calculation of the signal power using CWT in Matlab. Assume a signal of length N points with sampling frequency $f_{s}$. Using conventional approach, the power ...
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Given the Fourier Transform of a continuous signal how can I sketch the sampled signals discrete time fourier transform
I am given the frequency response for a continuous time signal $X(j\omega)$ = 2 at $\omega=0$ and 0 at $\omega = -10000\pi$ and $10000 \pi$. Looks like a triangle. I am told to sketch $X(e^{jw})$ ...
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Bandwidth of a given function
Suppose the signal given is $x(t)=(cos(5t)+e^{-2t})u(t)$ and the goal is to find the bandwidth of this signal. We know the bandwidth, $B$, is just $f_{max}-f_{min}$.
Our first step is taking the ...
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What is "Drift" in context of transformation concatenation?
My lecturer talked about transformation concatenation and he mentioned the "Drift" problem and that "bundle adjustment" may solve it. Since I could not find any information on it ...
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How to convert a line that goes through the origin into Hough space?
Assume that the lines are parameterized with an angle $\theta$ of the line normal and a distance $\rho$ from the origin:
For each of the lines in the image space below (left), draw the corresponding ...
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2D Fourier transform over mask of an image
I have an image, which has an inherent mask built into it. The exact shape isn't super important, but it looks something like a circ multiplied by a rect. I would like to calculate the 2D Fourier ...
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How do i compare the compression of different transforms?
I have to compare the compression capacity of different transformations on the same signal. The explanations were very brief, but i have to compare some energy thresholds(e.g. 50% of the total energy) ...
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Time Shifting, Reversal and Delay
For a signal, $s(t)$ undergoing multiple transformations of time scaling, reversal and delay, how should I approach the problem of finding the resultant output signal?
$$s\left(\pm \frac{t-t_0}{T}\...
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How to use inverse 2D Fourier transform to reconstruct the original image?
I have managed to get the forward Fourier transform of an image to the frequency space like so:
But I cannot for the life of me reconstruct the original image from the inverse Fourier transform of ...
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How to objectively measure how "good" a time-frequency representation of music is?
I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal ...
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Random projection with compressive sensing and hashing algorithms
I read that Random Projection matrices can be used in both Compressive Sensing and Locality Sensitive Hashing. I need simple explanation for the difference between applying Random Projection in both ...
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FFT for Arbitrary time history
I have two Time-Speed histories one is real ( real measurements) the other is synthetically generated using formula. I need to compare both in the frequency domain using FFT given that:
the time step ...
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simple explanation of rank transform and its relation to normal distribution
I tried to understand the rank transform, but I couldn't.
The first step common to all histogram remapping techniques is the transformation of the pixel intensity values of the given image via the ...
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How to alleviate the edging effect of the Hilbert transform?
I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
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Fourier transform of an aperiodic discrete-time signal
I have a signal of the form $x^{*}(-n+2)$. To derive the signal's Fourier transform I use The following properties of DFT: $x^{*}(n)=X^{*}(-\omega)$ and $x(n-k) = e^{-j\omega k}X(\omega)$
so the ...
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Amplitude-and phasefunctions for a system
I am studying a course in signalanalysis and have run into som trouble with a exercise.
I am to dimension the circuit below in such a way that the DC-amplification is 1 and that the frequencies $\...
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Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically with the signals in ROC?
Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically? Are we supposed to manipulate our O/P by multiplying any signal from ...
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What is the meaning of spectral contamination in image processing?
I resize the Multispectral image to perform IHS-to-RGB transformation. I used the Nearest Neigbour Interpolation method when resizing. While researching this issue, I saw that this is the best option ...
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Can a linear reconstruction in compressive sensing perform well?
I am trying to implement compressive sensing for grayscale 2D images, then reconstructing them using a multi-layer perceptron(MLP). It seems to perform well no matter how many layers I add or remove, ...
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Why does each node in the wavelet scattering transform split into multiple paths?
Why does each node in the wavelet scattering transform split into multiple paths as in this figure from Deep Scattering Spectrum?
I understand roughly what’s happening along a single path, but I don’...
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Why is incoherence important for compressive sensing?
The literature on compressive sensing (CS) frequently notes that CS relies on two principles: sparsity and incoherence. While I understand why the signal of interest should be sparse in some domain ...
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Application of the spherical Radon transform property in tomography
Let function $f$ be even and continuous on the unit sphere $S^n$. Let $R$-be a spherical Radon transform.
There is a known property:
$R(f^n)=f$ whenever $f$=constant.
What would this property mean in ...
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Scalograms in python
I am reading this paper to learning basic concepts of dsp and I want to reproduce the following scalogram of a test signal (fig 4.2 of the paper):
It has been produced from the discretization of the ...
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Difficulty with a Fourier Transform
What would be the best way to take the Fourier transform of
$$
f(t)\cdot \cos\big(\pi(t-1)\big)
$$
I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location ...
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How can we prove the correctness of the integration property of the Laplace transform?
I was going through an Electrical Engineering textbook for understanding the Laplace transform and came across the following proof for one of the properties of the Unilateral Laplace transform.
...
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Phase shift of discrete cosine transform (DCT)
The most common type of discrete cosine transform (DCT-II) is defined as
\begin{align}
X_k&=\sum_{n=0}^{N-1}x_n\cdot \cos\left(\frac{\pi}{N}\left(n+\frac{1}{2}\right)\cdot k\right)&\text{where ...
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multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function
I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$
I struggle a lot of hours trying to find the trick in item C.
Can anyone help please ?
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even symmetry of magnitude and odd symmetry of phase [closed]
I'll appreciate it if any of you guys could help me with this question:
Suppose that x(t) is a real signal, prove that the magnitude of its Fourier transform has even symmetry and its phase has odd ...
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How to test wavelet transforms?
One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?
MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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Understanding Parseval's Theorem with Discrete Wavelet Transform
I have difficulty to understand the results I get with implementing Parseval's Theorem in Python to DWT. I have the good results getting the Energy with Fourier transform and the time series in python:...
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1D DCT matlab code
I was writing MATLAB code to compute 1D DCT of sample y.
On computing DCT for y=[0,1,2], code generates coefficient ...
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How to transform a signal to go through specific points?
I have a 1d signal obtained using a Fourier based resample method (TDIFDZP) for which the resampled points don't necessarily go through the original samples. I want to transform the upsampled signal ...
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Question on N point DTFT - Fourier transform
I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal.
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What are the differences between the DWT and the MODWT?
What are the differences between the DWT (Discrete Wavelet Transform), which is the most classical algorithm and the Maximum Overlap Discrete Wavelet Trasnform (MODWT)?
Both these algorithm are ...
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KLT for an ECG Signal
I am currently searching for methods of feature extraction from an ECG signal and I've stumbled upon the Karhunen–Loeve Transform. I've read some papers and I think I get the basics but my question ...
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Downsampling, shifting, high pass and low pass filter commutativity
strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself.
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