# 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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11 views

### 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 ...
65 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. ...
82 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 ...
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:...
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 ...
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 ...
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.
22 views

### 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 ...
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 ...
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 ...
72 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. ...
110 views

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} ...
26 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 ...
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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 ...
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. ...
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 ...
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 ...
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......
3k views

### 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 ...
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 ...
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 ...
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 $d$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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,...
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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### 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)?
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 ...
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 ...
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 ...
3k views

### 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. ...
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, ...
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 ...
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 \$\...