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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Problem definition in KLT tracking

I am studying about the KLT tracker algorithm. In the KLT tracker, we can try to estimate the optical flow for corner points (because these are good features to track) between frames and the computed ...
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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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79 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:...
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149 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 ...
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1answer
34 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 ...
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69 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.
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security in biometrics

I read the following in one of the research papers: Cancelable biometrics using random projections can be implemented by multiplying a random matrix with a feature vector. The result is a cancelable ...
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65 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 ...
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27 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 ...
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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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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 ...
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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} ...
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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 ...
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Application of different SOCP Formulas

I'm studying the application of SOCP methods in Image restoration And I want to understand the difference between the two formulas of SOCP and how they are related. Standard form (1) : $$\min f^{t}x ...
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113 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{...
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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&...
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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 ...
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398 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 ...
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Image Transformation Functions to Identify if the Text in the Document Originally There or Just Synthetically Overlaid

I have a copy of scanned ancient dirty document and synthetically generated ancient dirty documents. I want to use Discrete Cosine Transform to characterize noise types existing in the document and ...
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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 ...
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50 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 ...
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38 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}...
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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 ...
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355 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 8x8 pixels image and I am applying the DCT to this sample. ...
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138 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 ...
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313 views

Any experiences for plotting a stationary wavelet transform?

I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides. There are very nice plots for CWTs, but does anyone know a technique for producing ...
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47 views

Is it correct to assume that $(-1)^n = \cos(\pi n)$ while computing the DTFT of $(-1)^n$?

$\cos(\pi n)$ fluctuates between $-1$ and $1$ depending on the values of $n$, and it would be the same as computing it with an exponential but the problem is that I just get part of the right answer......
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What is a Kravchuk transform and how is it related to Fourier transforms?

It has been stated here, that the the so-called Kravchuk transform is very important in the field of image processing and possibly in signal processing in general. I can hardly find any description ...
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419 views

How to achieve an arbitrary phase shift? [duplicate]

To help demonstrate why a time delay appears as a linear phase shift and not a constant phase shift I wanted to plot what a constant phase shift looks like. I have been looking at the Hilbert ...
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809 views

integration property of fourier series

Please help me sort this issue out. The integration property in Fourier series is as follows: So, for proving the above property, i took this approach: This is where my doubt is. Some books and ...
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1answer
106 views

Principal Component Analysis definition

I have just learned about this method, so I am not very familiar with it. As far as I know, Principal Component Anlysis (aka PCA) is used to transform a vector $x$ that belongs to a space of $d$ ...
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281 views

What is the correct order of operations for a 2D Haar wavelet decomposition?

The source code of iqdb contains a 2D Haar transform implementation. The author claims to have implemented it according to the paper "Fast Multiresolution Image Querying", which is freely available ...
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187 views

My impulse response does not tend to zero

I am doing an IFFT of frequency response data achieved with Simulation tools. When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
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224 views

High frequencies disappear when applying discrete wavelet transform

Trying to decompose and reconstruct a signal using a to some extent self-made implementation of DWT for some reason fails. The result looks highpass filtered and/or shifted. I wanted to write the code ...
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1answer
32 views

Time Setting of $z$ and Laplace Transforms

I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
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1answer
175 views

Calculating DTFT

When calculating DTFT of (1/2)^n u[n]. We evaluate the sum as follows: Please correct statements and answer questions below: 1) So to go from STEP 1 to STEP 2, the limits of the series are changed ...
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136 views

Region of Convergence

In attached image why does the ROC have these values for $$ X(z) = \frac{1}{1-\frac{1}{3}z^{-1}} - \frac{1}{1-2z^{-1}} ~~~~~,~~~~~ 1/3 < |z| < 2 $$ and for $$ Y(z) = \frac{5}{1-\frac{1}{3}z^...
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How to calculate Walsh hadamard transform for image patches of odd sizes?

I was reading this paper on optical flow, which as apart of the algorithm makes use Walsh-Hadamard transform on image patches of size 2r+1. So far, where ever I have looked, I could only find that ...
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215 views

CWT matlab function [closed]

i'm trying to apply the cwt function from matlab in the first graph and from the different articles that i've read i should get something that shows different peaks to determine the location of damage,...
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43 views

What are the constraints in design of discrete orthogonal wavelets?

Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank? So not all wavelets can be implemeted perfectly (invertible) with ...
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98 views

How to keep low frequencies in DCT

How can I keep a percentage r of the low frequencies of a Nx1 signal x using the Discrete Cosine Transform of it? Is it simply zeroing all but the first rN elements of DCT(x)?
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78 views

Nyquist Rate (Sampling Frequency) for $ {f}^{2} \left( x, y \right) $

We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$ Would it be correct to say that ...
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351 views

How can I calculate the Number of bins per octave?

I am trying to calculate the Constant Q Transform for Monophonic audio using Python. The Python has the library to calculate the CQT , the default value of num_bins_per_octave is 12. How would one ...
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2answers
232 views

Band-limited random signal with arbitrary distribution?

I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
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Show others how I hear myself

Sooo .. I've been thinking about this stuff. We all know that we sound different from what we hear of our own voice. It is easy to find out how others hear us by recording oneself and listen to it. ...
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411 views

Extreme quantization of audio

I would like to take an audio sample and reduce it to a very limited set of numbers, with one value for amplitude and another for length. Example: I want to find the dimensions of the red boxes, ...
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144 views

Calculating fourier transform

I have just recently started doing fourier transforms and I'm a little confused. Can someone walk me through in detail how to calculate the Fourier transform of I'm not looking for answer, just an ...
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1answer
46 views

How is the ROC of a transform function determined?

Suppose I have $x[n]$ and $y[n]$, and I calculate their respective Z-transforms $X(z)$ and $Y(z)$ as well as their respective ROCs. Calculating $H(z)$ is as simple as calculating the quotient of $\...
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34 views

Denoising before or after Geometric Transform?

I am working on a image which needs denoising (bilateral filter) and a geometric transformation. I am not sure in which order these filters should be applied. Personally I think it is better to use ...

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