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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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How does the shape of a frequency domain function (Fourier Transformed time domain function) change when a time shift is applied in the time domain?

When there is a time shift (or delay) in the time domain on a function, the Fourier transform gets multiplied by an exponential which corresponds to a phase shift on the original frequency domain ...
quack's user avatar
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Normalisation of Complex Morlet Wavelet

I am currently writing an essay on Wavelet transforms, and as part of such, I am trying to show that the Morlet wavelet satisfies the standard criteria: $$ \int^\infty_{-\infty} \psi(t) dt = 0 $$ $$ \...
Isaac Mortiboy's user avatar
4 votes
1 answer
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What are some good questions for a graduate level signal processing course?

I am currently taking an graduate-level Advanced Signal Processing class and I have a midterm soon. However, the midterm is not only open-book but it is also open-internet and untimed. Now I have no ...
Sherlock Rozman's user avatar
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How do i know which operations transformed a signal?

I am doing an undergrad assignment and one of the exercises is as follows: Given the following signal $x(t)$: and another signal $y(t)$ which was transformed from $x(t)$: Describe $y(t)$ in function ...
heresthebuzz's user avatar
1 vote
1 answer
90 views

Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the ...
Mikayla Eckel Cifrese's user avatar
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28 views

Issues obtaining Clarke Park transform

I have a three-phase electric signal and I've been asked to obtain its Clarke-Park transform (also called direct-quadrature-zero or dq0 transformation). I'm using this Python library, and I've gotten ...
J. Maria's user avatar
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Correct low pass filter after applying discrete cosine transform

I am working on the compression of a bmp image using discrete cosine transform. First, I split the image into 4x4 blocks and then apply a DCT to each block. I know that low frequency coefficents (the ...
purecobalt's user avatar
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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.
holder fo's user avatar
2 votes
1 answer
100 views

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 ...
Hao Wu's user avatar
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2 votes
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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 ...
Sahil Sharma's user avatar
1 vote
1 answer
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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 ...
Sidharth Ghoshal's user avatar
3 votes
1 answer
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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 ...
Logan R. Kearsley's user avatar
1 vote
0 answers
27 views

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 ...
Nyquist-er's user avatar
2 votes
1 answer
742 views

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:...
Joseph's user avatar
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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
IMAN RAMZANPOOR's user avatar
2 votes
2 answers
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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 $l^{th}$...
ABB's user avatar
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1 answer
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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) = \...
jeff yan's user avatar
3 votes
3 answers
513 views

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 ...
Lobster3221's user avatar
3 votes
2 answers
326 views

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 ...
M-S's user avatar
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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 $X(e^{jw})$ ...
Caleb Burke's user avatar
0 votes
1 answer
562 views

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 ...
Alexander Michalak's user avatar
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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 ...
vesii's user avatar
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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 ...
vesii's user avatar
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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 ...
user2551700's user avatar
1 vote
1 answer
38 views

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) ...
conopizda2's user avatar
2 votes
1 answer
177 views

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}\...
kdkvcm's user avatar
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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 ...
user avatar
1 vote
2 answers
205 views

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 ...
Sevag's user avatar
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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 ...
Fatma Diab's user avatar
-1 votes
1 answer
169 views

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 ...
Khalid's user avatar
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1 answer
574 views

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 ...
Noha's user avatar
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3 votes
1 answer
2k views

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 ...
Eric94's user avatar
  • 33
0 votes
1 answer
414 views

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 ...
Việt Nguyễn's user avatar
1 vote
1 answer
43 views

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 $\...
Aedrha's user avatar
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0 answers
22 views

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 ...
Husnain Afzal's user avatar
0 votes
1 answer
96 views

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 ...
Sun's user avatar
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3 votes
1 answer
89 views

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, ...
Ahmed Mokhtar's user avatar
-1 votes
1 answer
170 views

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’...
Churchjm 's user avatar
3 votes
1 answer
414 views

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 ...
blerner's user avatar
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1 vote
0 answers
24 views

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 ...
User 12345's user avatar
4 votes
1 answer
6k views

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 ...
Gaussian's user avatar
1 vote
2 answers
228 views

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 ...
Minato Namikaze's user avatar
3 votes
1 answer
718 views

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. ...
Aditya's user avatar
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4 votes
1 answer
411 views

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 ...
chicken_game's user avatar
0 votes
1 answer
76 views

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 ?
Ilya.K.'s user avatar
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1 vote
0 answers
342 views

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 ...
Gertrud Schmidt's user avatar
1 vote
2 answers
195 views

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. ...
OverLordGoldDragon's user avatar
1 vote
3 answers
97 views

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 ...
ashkan's user avatar
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3 votes
1 answer
500 views

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:...
eemilk's user avatar
  • 133
2 votes
2 answers
1k views

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 ...
Prabal Devkota's user avatar

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