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.

Filter by
Sorted by
Tagged with
1
vote
1answer
27 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) ...
1
vote
1answer
35 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}\...
0
votes
0answers
28 views

How to do stretching Image distortion transformation

I have an assignment to transform an image like this: I have done with twirling, fisheye, bulge, but I'm having a hard time finding the right formulas for those effects. here is my code for twirling: ...
1
vote
2answers
130 views

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 ...
0
votes
0answers
13 views

Are the sparsity of transform coefficients comparable when their frequency ranges are different?

I have obtained a graph-based Fourier transform from an optimization problem, and for evaluating the sparsity of transform coefficients, I was going to compare it with other transform coefficients ...
0
votes
0answers
15 views

How do you find the length of a constant q transform window in librosa?

I am working on a machine learning project to transcribe classical chamber music. I have a collection of audio files and for each time interval, I have data which tells me which notes are being played....
1
vote
2answers
83 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 ...
0
votes
0answers
47 views

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 ...
0
votes
1answer
43 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 ...
0
votes
0answers
31 views

How to effectively stationarise non-periodic wave signals?

I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
0
votes
1answer
76 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 ...
3
votes
1answer
146 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 ...
0
votes
1answer
49 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 ...
1
vote
1answer
38 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 $\...
0
votes
0answers
51 views

Inverse process for homography matrix (estimating image transformation at arbitrary camera pose)

The pose of camera at given image can be estimated by decomposing a homography matrix. I want to know if there is a process where given camera at certain arbitrary pose, we could compute the how an ...
0
votes
0answers
40 views

Perspective Correction by re-positioning Camera

So perspective correction is a process of applying transformation to image to make it appear less perspective. I would like to know if there is a process of obtaining similar transformation to enable ...
0
votes
0answers
20 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 ...
0
votes
1answer
42 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 ...
1
vote
1answer
62 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, ...
1
vote
1answer
63 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 https://arxiv.org/abs/1304.6763? I understand roughly what’s happening along a single path, but ...
2
votes
1answer
70 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 ...
1
vote
0answers
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 ...
2
votes
1answer
933 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 ...
1
vote
2answers
221 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 ...
2
votes
1answer
148 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. ...
4
votes
1answer
110 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 ...
0
votes
1answer
51 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 ?
1
vote
0answers
50 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 ...
0
votes
2answers
93 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. ...
1
vote
3answers
94 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 ...
3
votes
1answer
189 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:...
2
votes
2answers
590 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 ...
0
votes
1answer
39 views

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 ...
1
vote
2answers
125 views

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.
0
votes
1answer
254 views

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 ...
0
votes
1answer
47 views

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 ...
4
votes
1answer
117 views

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. ...
1
vote
2answers
220 views

Question about Hilbert transform

Hilbert transform of a function $g(t)$ which is defined in time domain, would result in another function in time domain. Is there any other transformation like Hilbert that the results be in time ...
1
vote
2answers
347 views

Is there an easy way to translate a Fourier transform table from angular frequency $\omega$ to Hertz $f$?

I have a table with transform operations, e.g. scaling: \begin{equation} \tag{0} \label{0} x(at) \iff \frac{1}{a} X(\frac{\omega}{a}) \end{equation} or frequency shifting: \begin{equation}\tag{1} ...
1
vote
0answers
36 views

Difference between these two Continuous Wavelet Transforms?

I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
0
votes
2answers
370 views

How to properly convert from dB back to amplitude

I am new to signal processing. I have a signal that I want to convert to dB, process and then transform back. My understanding of the transformation to dB scale is $X_\mathrm{db} = 20 \cdot \mathrm{...
2
votes
0answers
68 views

Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
0
votes
2answers
68 views

How do wavelet levels depend on one another?

I am working with wavelets for my thesis, and I would like to know if there is an intuitive dependency between the levels of a DWT. To make it clear: The DWT performs a convolution, and then the ...
1
vote
1answer
867 views

Discrete Cosine Transform (DCT) Coefficient Distribution

I have two images : Original Image Binarize Image I have applied Discrete Cosine Transform to the two images by dividing the 256x256 image into 8x8 blocks. After, I want to compare their DCT ...
4
votes
0answers
7k views

Plotting a scalogram of a signal's Continuous Wavelet Transform (CWT) in python

So I've been learning about wavelets for a few weeks because I'd like to use them in a research project I'm working on and I've been trying to grasp the general ideas behind them.I've been struggling ...
0
votes
1answer
92 views

Number of datapoints after decimation in discrete wavelet wavelet analysis

I am following an example provided by MATLAB on 1-D wavelet decomposition (DWT). The number of datapoints is 10000. If we do a level 3 decomposition following a similar example provided by MATLAB ...
0
votes
1answer
64 views

Does constant Q transform have linearity property in the transformed domain?

With FFT, I sometimes take advantage of the fact that I can pre-calculate a signals Fourier Transform, and then you can add the noise in the spectral domain: $$ \mathscr{F} (x[n] + h[n]) = \mathscr{F}...
1
vote
0answers
90 views

How to simulate Zoom, Pan, Tilt transformations? [closed]

Say we are looking at a football field from a broadcast view. To give us another tool, we also have a transform of that view to a topdown view. So our two views are like so: How would one simulate ...
2
votes
2answers
784 views

DCT - Coefficients and Basis Function

I am trying to understand how the Discrete Cosine Transformation works but I am not sure if I am at the right road. Assuming that I have an $8\times8$ pixels image and I am applying the DCT to this ...
1
vote
1answer
389 views

Two different answers while doing Inverse Z-transform

Given, $$X(z) = \frac{z}{3z^2 - 4z + 1}$$ Question 1 I need to calculate inverse z-transform for ROC $|z|>1$ When I try to calculate inverse $z$-transform using partial fraction of $X(z)$ and ...

1
2 3 4 5