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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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1answer
137 views

Significance of sequency ordering in Walsh-Hadamard matrices

So I've been doing some reading into Hadamard and related matrices (Slant, Walsh, , and have observed that there are three typical "orderings" of the rows based on various criterion. E.g. "Natural", "...
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2answers
41 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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0answers
26 views

How to simulate Zoom, Pan, Tilt transformations? [on hold]

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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2k views

Fourier transform 4 times = original function (from Bracewell book)

I was glancing through "The Fourier Transform & Its Applications" by Ronald Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the FT of a function 4 ...
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17 views

Image Processing Perspective Transform

This youtube video shows the current world record for smb1 speedrun, but it is recorded from a phone on a CRT TV. https://www.youtube.com/watch?v=IuVLtaB8uQk Is it possible through perspective ...
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1answer
39 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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1answer
500 views

Questions related to Laplace Transform

While studying Laplace transform, I also some questions which I want to understand: a) We used to say that Laplace transform include both real and imaginary part whereas in Fourier transform we ...
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1answer
51 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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1answer
827 views

Getting frequency content at different times from discrete wavelet transform coeffs

After being away from DSP for a long time, I am trying to familiarize myself with wavelet transform. Here is what I (think) have understood so far: Wavelet transform provides you high time resolution ...
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1answer
1k views

How to perform a Stockwell Transform on a 2D matrix

I was looking at performing a Stockwell transform on a matrix (or an image as it has two directions - the matrix I am interested in has a spatial dimension and a time dimension, but this should make ...
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1answer
97 views

Critically Sampled Laplacian Pyramid from 2nd Generation Wavelet

I'd like to know if a technique I have in mind is already used and has a name I can look up, and whether it is likely to work and be useful! My aim is to produce a discrete wavelet transform that is ...
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75 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
320 views

Biquad coefficients using Magnitude (or Phase) Invariance Mapping Method

I'm trying MIM (Magnitude Invariance Method) and PIM (Phase Invariance Method) for to improve biquad LPF response at low sampling rates. I'm looking some help and examples of usage if available. ...
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1answer
135 views

Recursive DCT implementation

I am trying to understand the recursive implementation of the DCT on the input signal (used for LMS filtering) according to the pictures below. The pictures and formulas are taken from the paper: "...
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1answer
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 ...
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1answer
58 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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1answer
356 views

Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
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11k views

Feature extraction/reduction using DWT

For a given time series which is n timestamps in length, we can take Discrete Wavelet Transform (using 'Haar' wavelets), then we get (for an example, in Python) - ...
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44 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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1k views

Recovering an image using IDCT through DCT coefficients

I have computed the discrete cosine transform (DCT) of an image in MATLAB. I got a matrix of discrete cosine transform coefficients in the workspace. How can I recover the original image from its ...
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1answer
83 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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1answer
74 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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3answers
842 views

IIR Hilbert Transformer

I'm beginning to explore discrete Hilbert transformers - ways to achieve 90°. phase shift across a band of perhaps 6 kHz at a 44.1 kHz sampling rate. I'm trying to stick with IIR filters in order to ...
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20 views

How can I find inverse Z transform using synthetic division method when Region of convergence is bounded rather than right sided or left sided?

Explanation of synthetic division method Above example has region of convergence of type mod(z)>mod(a) I want to solve problems when region of convergence of type mod(e)>mod(z)>mod(d)
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Haar series approximation of a function?

I'm trying to code the Haar wavelet approximation of a function. I'm a complete newbie. Edit Below is a pseudo-code of my algorithm for $f: [0,10] \to \mathbb R$, $f(x)=x$. I picked it here and ...
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3answers
243 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
102 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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2answers
149 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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2answers
87 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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0answers
9 views

How to warp and enlarge the center of an image?

I am trying to smoothly enlarge the center part of an image. The Skimage code that I use need an inverse map that specifies location of input pixels that will occur at the output pixel location. If I ...
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1answer
215 views

Wavelet central frequency

What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet? Thanks.
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1answer
106 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
248 views

Usefulness of Matrix Notation for Linear Periodically Time Variant Transformations

I am quit puzzled about a notation I found in Gardner's 1986 book titled Introduction to Random Processes. It is in the chapter on Cyclostationary Processes at section 12.4 which pertains to Linear ...
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1answer
31 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
34 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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0answers
38 views

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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3answers
480 views

Question about z transform

After studying z transform from different books and literature on internet I want to ask few which makes me confuse. a) From the Discrete Time Fourier Transform we have drive equation for z ...
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0answers
22 views

Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
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1answer
103 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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0answers
36 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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1answer
56 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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1answer
48 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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0answers
119 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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0answers
256 views

Why does the Stationary Wavelet Transform shift this image?

I am running a stationary wavelet transformation on a brain image. I can't understand why it shifts with each level so that the image is no longer centered. You can see that the X component shifts to ...
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2answers
133 views

FFT equivalent for generalized unitary transforms

The DFT has the FFT, Hadamard transform has the Fast Hadamard Transform and so do a number of other unitary transforms (operators). Is there or has there been an attempt at creating FFT style ...
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1answer
4k views

Discrete wavelet transform; how to interpret approximation and detail coefficients?

I am trying to understand Wavelet transform. So far I have understood the basic theory of it. But I am not able to get my head around how to interpret both coefficients. I am using PyWavelets ...
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3answers
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. ...
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1answer
215 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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1answer
34 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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1answer
2k views

What is the difference between Constant-Q Transform and Wavelet Transform and which is better

i have been seeking for a better Transform than STFT with high overleaping. The Transform should more suitble for the human auditory system. And i learned that there are at least 3 Methods i may use ...