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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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12 views

What wavelet should i use to analyze harmonic function?

If i have the following signal: $$ s(t) = cos\left [ t\cdot \left (\frac{a}{2}t+b \right ) \right ] $$ What is the best family of wavelet to analize the signal, and what is its scale range? Do i ...
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26 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 ...
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2answers
66 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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18 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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41 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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73 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
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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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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81 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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23 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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291 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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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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90 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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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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2answers
91 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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1answer
116 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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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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53 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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36 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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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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116 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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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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57 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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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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131 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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152 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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230 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
76 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
36 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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32 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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100 views

Using the given identities, find the inverse DTFT

Using the given identities, $ a^nu[n]$ <===> $\frac{1}{(1-ae^{-jw})}$ $\delta[n-k]$ <===> $e^{-jwk}$ Find the inverse DTFT of, $ H(e^{jw}) = B \frac{e^{-jw}}{(1-ae^{-jw})}$ my attempt: $ ...
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226 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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205 views

What is the exact meaning of the output of the Discrete Fourier Transform

I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
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2answers
994 views

Transform RGB image to *look like* Infrared

Context: I'm trying to improve a pose estimation model so that it works better when my camera is in Infrared mode. Unfortunately I only have RGB images to train on. I realize that you can't convert ...
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1k views

3D world homography matrix calculation

I have a matrix in (x,y,z) coordinates and also i have a transformed version like (x_new,y_new,z_new). I need to calculate a transformation matrix that can transform (x,y,z) to (x_new,y_new,z_new). ...
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40 views

Unclear inverse Z-transform of $G(z) = \frac{1-p}{z-p}$

In this paper on page 5 equation (10) is supposed to be the reverse z-transform of equation (5) on page 4. $$\frac{U(z)}{\bar{U}(z)} = G(z) = \frac{1-p}{z-p} \quad \leftrightarrow \quad u(k) = \bar{...
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981 views

Hilbert transform of sinusoid — apparent contradiction

The arrow "$\xrightarrow{\mathcal H}$" denotes a Hilbert transform: $$\cos(\omega t)\xrightarrow{\mathcal H} \sin(\omega t)$$ happiness. But $$\cos(\omega t) = \cos(-\omega t) \xrightarrow{\...
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1answer
136 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
161 views

Computational burden of EMD/Huang-Hilbert vs wavelet

I am working on an online application of signal processing and pattern recognition. It involves sampling the signal at 2 MS/s, extracting features and classifying. My classifier has pretty good ...
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1answer
163 views

Implementing the DWT

I have been given the task to implement the 5/3 CDF transform for image compression. Given that the impulse response for the low and high pass are: $h_1 = [-0.5, 1 ,-0.5]$ (High Pass) $h_2 = [-0....
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84 views

Calculating gyroscope data from accelerometer and attitude data

I am currently collecting accelerometer and attitude data using smartphone sensors. Data is collected at 100Hz over 2.5 seconds. Of which there are 250 accelerometer points and 250 points representing ...
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1answer
5k 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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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 ...
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882 views

Conditions for which the Hilbert transform returns a correct phase

I'm quite new to signal analysis, and I'm currently trying to understand under which conditions a Hilbert transform can be used to compute the correct instantaneous phase and enveloppe of a given ...
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1answer
91 views

What is the general formula for radon back projection for a javascript implementation?

I'm aiming to implement a simulation of computed tomography back projection in javascript/HTML5 canvas. Trying to figure the correct approach for doing a back projections and I have been studying the ...
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1answer
43 views

What is the meaning of negative second for a Morlet wavelet?

I kind of familiar with wavelet transform (I just used it in code but do not have a deep understanding about it). I've been reading an article and came across this sentence: where 4Fs is the ...
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1answer
36 views

HHT : Toning down noisy data

I've recently asked a question on stack overflow asking for different topics one can visit to solve the problem of wave re-construction. One of the recommended solutions was to implement the Hilbert-...
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1answer
55 views

Is there a special case in which wave atoms convert to curvelets?

I'm new to multi scale transformations. I was wondering if there is a special case where wave atom converts to curvelet transform? Can I use wave atom parameters to have curvelet properties?