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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Question about vanishing moments in wavelet tranforms

I am reading the book Noise reduction by wavelet thresholding by Maarten Jansen. About vanishing moments, it reads To create a really sparse representation, we try to make coefficients that ...
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49 views

Daubechies wavelet transform

i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which ...
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Interpretation of Diagonal detail wavelets

I am a statistics grad student, and I have just begun exploring the topic of wavelet regression (specifically, Haar wavelets for discrete functions). I understand the generalization from a one ...
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Can anyone explain how does CZT (Chirp Z Transform) really help in 'spectral zooming'?

I found some explanation alongwith the Matlab Code here: http://prod.sandia.gov/techlib/access-control.cgi/2005/057084.pdf but I can't figure out, without a good example, why would this result in ...
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35 views

What is the name of this transform similar to the Radon transform?

I have a 2D image (obtained using computed tomography) that I'm "transforming" for image segmentation purposes, and I'm looking for a formal way of describing the transformation I'm doing. The ...
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61 views

Implementing wavelet transform for finding transients in the power supply

I am new to the concept of wavelet transforms. Can somebody please help me in understanding this ? and also how to implement it in c. Is Short term Fourier transform more efficient than Wavelet ...
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42 views

Is DCT (Discrete Cosine Transform) of Type-2 lossless or lossy?

As I know, in general, the DCT is lossless. But I'm not exactly sure about Type-2 of DCT. Is it lossless or lossy?
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36 views

Fourier transform 4 times = original function (2D and higher)

The Signal Processing SE post linked below shows how the Fourier Transform applied 4 times to a 1D function returns the original function, i.e. F{ F{ F{ F{ g(x) } } } } = g(x) Link to 1D case: ...
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19 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 ...
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18 views

Retrieving camera orientation from DLT parameters

I currently have 12 DLT parameters to map 3D points to 2D pixels, the projection/conversion works nicely. Now, I am able to retrieve the camera position from the parameters using equation [25] from ...
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24 views

How is the luminance vector calculated for these linear matrix transforms

In the article "Matrix Operations for Image Processing" by Paul Haeberli there is an example described using a matrix to alter the saturation of an image. In the example given the author first ...
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Multiplication property DTFT

I was truing to solve an example of DTFT which is following multiplication property. The problem is $$ a^n \sin(\omega_0 n) u[n]$$ we know that the definition of DTFT is $$ X(j \omega) = \sum _ ...
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25 views

Multiplier in digital signal processing?

whenever we start working on Discrete Cosine Transform(DCT), Loeffler algorithm a key role. Furthur if we approach hardware implementation of this algorithm, we find methods based on Distributed ...
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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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1answer
21 views

Finding Laplace Transform without ROC

While studying Laplace Transform i found that region of convergence (ROC) is important because for some problems we have same Laplace Transform but different ROC helps us to take correct inverse ...
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29 views

Confusion in proof of Inverse Laplace Transform

For the proof of inverse Laplace transform, we change the integral from $\omega$ to $s$. I want to know the reason why we need to change the integral?
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35 views

Laplace Transform of $-e^{-at}u(-t)$

I have found a problem in applying Laplace Transform to $-e^{-at}u(-t)$ I am doing these steps: $$ = - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$ = - \int_{-\infty}^{0} e^{-at} ...
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46 views

Why we take Laplace Transform of functions which converged using Fourier Transform

There are several functions for which we know that Fourier Transform will exist but still we calculate its Laplace Transform. Can I know the reason why we need to take Laplace transform for which we ...
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37 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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59 views

Fourier Transform of exponential

While solving Example 4.1 of Signals and Systems by Alan Oppenheim. Example 4.1 is: $$ x(t)=e^{-at}u(t), a>0$$ and the transform I get is: $$ X(j\omega)\frac{1}{a+j\omega}, a>0$$ The problem is ...
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39 views

Confusion in basics of Laplace Transform

I have few confusions while starting Laplace Transform. So far I have studied, Fourier series and Fourier Transform. The basic difference which I found from different books is Fourier Transform is ...
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28 views

Are Fractional Fourier transform applicable to non linear signals

I am aware that generally fourier analysis is applicable to linear signals from the literature papers. I wanted to know if fractional fourier transforms are also applicable to only linear signals ...
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Image transformation where a curve becomes a straight line [closed]

Suppose that I have the green curve (image attached for visualization), values stored in a vector and I want to transform the image such that the curve becomes a straight horizontal line. So if the ...
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Fourier Transform of image convoluting with kernel [closed]

edit: clarifying question. ...
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selection criteria for different projections

I need to know the percentage of height of human body parts, I have the following information that I used: my issue in selecting human which was not appeared straightforward (upright) with ...
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2D Haar Transform Computational Complexity

I want to learn the computational complexity of the 2D Discrete Haar (Wavelet) Transform (DHWT). The number of operations (divisions, summations etc.) is the main focus. I think there are many ...
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214 views

Why is a wavelet transform implemented as a filter bank?

The mother wavelet function $\psi(t)$ must satisfy the following: $$\int\limits_{-\infty}^{+\infty} \frac{|\psi(\omega)|^2}{\omega} d \omega < +\infty,$$ $$\psi ( \omega ) \bigg|_{ \omega =0} ...
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79 views

Difference between summation of motion components and IFFT?

I have a problem using the IFFT command. I want to see if i can go from the frequency domain to the time domain of a signal. I wanted to test this in two parts: 1) first creating a wave time ...
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48 views

Equation visualization of complex sinusoid function

I'm trying to learn Fourier Transform & Signal I can visualize how this expression $ A \sin(2 \pi f t)$ could turn into that curvy sinusoidal signal. But i couldn't visualize how $F(\nu)e^{2 \pi ...
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135 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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74 views

Generating Wavelet family matrixes

We have unnormalized Haar matrix which, is for example, H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1] After normalizing it, we use for haar transform. I know how to ...
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21 views

Transformation validation

I am trying to see the validity of my geometric transformation, by imposing a point I got from a tracker in the original image and superimposing it on the image after the transformations. The point ...
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1answer
53 views

Audio phase shift using Hartley Transform

I want to shift the response phase of an audio signal (float array, length N, value range -1..1). I'm about using Fast Hartley Transform to transform it to the frequency-domain, process phase shift, ...
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37 views

STFT multiplied with Gaussian Impulse vs STFT multiplied by unit height rectangular impulse

I am currently analysing my signal by looking at its spectrogram to determine the sinusoidal frequency content at the local sections of my signal overtime. I can do my spectrogram in 2 ways: ...
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239 views

How condition for existence of Fourier transform is valid?

The condition for Discrete time Fourier transform to exist for function $f(n)$ is given as $$\sum_{-\infty}^\infty |f(n)| < \infty.$$ In case of continuous Fourier transform the difference is ...
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Finding filaments in high dimensional space

I have unit vectors in a high-dimensional space (~300) that are non-uniformly distributed over this hypersphere. There is physical meaning when the vectors are clustered together, but I'm ...
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120 views

Whether Fourier transform formula be considered as Convolution or Correlation?

The expression for Fourier transform is given as $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^{-j \omega t} \ dt \tag{1}$$ Now, let one function be $f(x)$ and other be $e^{j\omega t}$ ...
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53 views

Why Z-transform is considered as separate transform?

The mathematical formula of the Laplace and Z transforms are same with just one difference. I.e. in the first we use $t$ for continuous-time signal and in the latter uses $n$ for discrete-time ...
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36 views

Help with Hankel Tranform filters

I found a filter for Hankel Transform . As far as i understand this is effectively used as an approximation for J0(x) and J1(x) . But how will the change in input affect these filter terms (eg J0(r) ...
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31 views

Is affine the right transformation for coordinate change?

I have a video which was used in a tracking program. In that program the object being tracked receives per frame X,Y coordinates which are not the same as in the my video. I have a few coordinates ...
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1answer
59 views

Inverse z transform - contour integration

Here is my task: Find inverse z transform of $X(z)=\frac{1}{2-3z}$, if $|z|>\frac{2}{3}$ I need to find it using definition formula, $x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$. How can I ...
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78 views

Inverse z transform - help

How can I find inverse z transform of $$X(z)=\frac{5}{(z-2)^{2}}$$ ? It is known that x[n] is causal. EDIT: Here is what I have done. Since signal x(n) is causal, convergence of z transform of that ...
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2answers
120 views

Power Spectral Density computation and units

I want to make some calculs of power spectral densité of signal. For example a real voltage signal (physical unit : $V$) in time $g(t)$, its fourier transform $G(f)$ and $S_g(f)$. As far as I ...
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81 views

Sampling Continuous-Time Signal

This my homework: Input signal to system is: where H(exp(jw)) is transfer function of ideal low pass filter with cutoff frequency wg=3*pi/4 and zero phase characteristic. Sampling in A/D ...
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205 views

Help for programming CWT using complex morlet wavelet?

Here is my code for continuous wavelet transform using complex morlet wavelet. But it's not giving accurate result..Please anybody help to rectify my mistakes..thanks in advance :) ...
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2answers
137 views

How to transform or distort or skew a rectangular image to fit arbitrary quad

I have a rectangular image which need to transform so the image fits an arbitrary convex quad. Easy? Except I have an important constraint, the features on the original image must maintain their ...
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1answer
75 views

Do signals with a Fourier transform with discontinuities or zero amplitude (in some frequencies) have Laplace transform?

I am reading a book on Laplace transform, and in the section on the convergence of Laplace transform for various signals the following theorem is stated, without any proof : If a signal's Fourier ...
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62 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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29 views

Haar transform definition

I am trying to understand Haar transform of simple vector of numbers. Some references I found say, that first level transform of $ X = (4,6,8,10,13,9,3,3)$ will be $\sqrt{2}(5,9,11,3, -1,-1,2,0)$. ...
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Conceptual queston on Z transforms and time series model (Part2)

I am learning the fundamentals of signal processing and time series models and I am having a hard time to follow due to lack of basics related to $z$ transforms and autoregressive model. I am facing ...