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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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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52 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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70 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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16 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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75 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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33 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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20 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
41 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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1answer
21 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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3answers
152 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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49 views

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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1answer
114 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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48 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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1answer
33 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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22 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
50 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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2answers
71 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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1answer
61 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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77 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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128 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
115 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
67 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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1answer
58 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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26 views

$ICA used for feature reduction on images

I am working on a semestral project that consists of different parts in image segmentation. I am developing part with transformation of image features. As reference I have PCA for dimensionality ...
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1answer
28 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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37 views

Constant-Q transform - summing complex DFT coefficients vs. summing DFT magnitudes

The constant-Q transform computes a spectrum on a logarithmic frequency axis. When analyzing music signals, this can be a more meaningful representation than the Discrete Fourier Transform (DFT), as ...
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69 views

Why do we use Hilbert Transform in discrete time domain?

I have few questions regarding hilbert transform, Questions are as follows: 1)What are the benifits of using hilbert transform hardware and software point of view? 2)Cannot we use any other digital ...
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32 views

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 ...
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37 views

High error due to resample function in MATLAB

I am working on training the output of the wavelet transform of a signal using a neural network in MATLAB. So I decided to use 3 layer ...
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1answer
96 views

Why doesn't JPEG use 1D DCT for image compression?

I know that JPEG uses 2D dct and splits the images in 8x8 blocks. Why doesn't it simply split the image in one-dimensional vectors in $\mathbb{R}^{64}$? Wouldn't it simplify the math? My guess is that ...
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1answer
175 views

How to extract IF (instantaneous frequency) from Discrete Hilbert Transform?

The continuous time Hilbert transform is $$\hat x(t) := x(t) + j\left( p.v. \left\{\frac{1}{t\pi} \ast x \right\} (t)\right)$$ where $$ \theta(t) = \tan^{-1}\left( \frac{ p.v. \left\{\frac{1}{t\pi} ...
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1answer
83 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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170 views

Analysis and algorithmic complexity of the Constant Q transform

Here I am again (Implementation of the constant Q transform + property questions) :) I was reading this paper on a constant-q transform algorithm, where they managed to turn the following equation ...
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1answer
126 views

FFT on XY data points [closed]

Are there any algorithms out there that can do a FFT of 2D or XY data (not sure of the exact terminology here), I don't mean XY data like in a graph I mean XY/2D data points like a circle or a smiley ...
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1answer
98 views

Polarity inversion in frequency domain (polar coordinates)

I don't fully grasp how polarity inversion is performed in the polar coordinates of frequency domain. The frequency components of the signal do not change, so the amplitude part is going to stay ...
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107 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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1answer
119 views

Intuitively explain Bi-linear time frequency distributions, someone please?

I have a fairly good understanding of Wavelet Analysis, but what are these bilinear distributions and how do they differ from Wavelet Transform?
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2answers
75 views

Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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40 views

Speech features that can be inverted?

I am trying to figure out speech features that can be inverted to recover the audio back with no loss or as less loss as possible. I am currently using the power spectrum which is completely ...
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66 views

Fourier Transform Time Scaling

I edited the initial question to make it general and thus applicable in more situations. If the Fourier Transform of $x(t^2)$ is some function of $\omega^2$. Then what is the Fourier Transform of ...
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1answer
225 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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2answers
236 views

Compensate for phase shift of Hilbert transform

I'm using Octave and trying to use the "instfreq" function from the time frequency toolbox which requires an analytic signal input. To get this analytic signal I'm using the Octave function "hilbert" ...
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1answer
159 views

Transformed Direct Form II filter: Z transform: reduce multiplications

In the diagram below there are three multiplication operations required to compute each filter output sample. I'd like to draw a block diagram of an equivalent filter but requiring fewer than three ...
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59 views

Connection with system analysis and laplace&Z transform

Laplace&Z transform is just frequency analysis of a system with a multiplication of decaying exponential. We analyse frequency with varying Laplace Exponential, which can be seen in the formula ...
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1answer
710 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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143 views

Correct image rotation/scale/moving change

I'm pretty new to Image Processing and am using MatLab. I have an problem were I take an image of light passing trough an set of optical fibers (bundled together) and one were I pass laser energy ...
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1answer
376 views

Computing narrowband spectrograms using MATLAB [closed]

I'm having an assignment of computing narrowband spectrograms using MATLAB. And I totally have no idea about the code. Can someone help me writing the code and explaining what's going on to me. Lots ...
2
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2answers
223 views

What does boundary discontinuity in DFT imply?

I have been studying about boundary discontinuity in DFT and why it is not used as transform in image compression. What i understand is that DFT is N periodic and that causes a discontinuity at the ...
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Continuous Wavelet Transform with Scipy.signal: what is parameter “widths” in cwt() function? How do time-frequency?

I search to display a time-frequency signal with an original discrete temporal signal (sampling step = 0.001sec). I use Python and the library Scipy.signal. I use the function ...
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1answer
42 views

Matrix form of STFT

IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...