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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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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0answers
15 views

Calculate the Lyaponuv spectra of an EGG time series [on hold]

I am trying to implementing some results from an article that use this data. There it considers that each TXT-file consists of 4096 samples of one EEG time series.  For the algorithm ...
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2answers
34 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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1answer
71 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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10 views

Wavelet transform on vibrations

I am working on wavelet transformation on vibration signals. I have data with displacement values, I had performed 'wavedec' function on my signal. I obtained the corresponding aprox. coefs and det. ...
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34 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
97 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
56 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
49 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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0answers
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
23 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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35 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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44 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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0answers
25 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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0answers
33 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
71 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
142 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
64 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
124 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
79 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
84 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 ...
3
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0answers
90 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
112 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
70 views

Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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0answers
36 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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2answers
64 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
159 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
166 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
143 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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2answers
54 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
555 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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0answers
109 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
328 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
211 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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3answers
2k views

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
37 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? ...
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2answers
59 views

Complex numbers in a frequency domain of a 2D image [duplicate]

I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere. How are frequency domain and ...
2
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1answer
56 views

Is there an analogue of coherence between data sets related by a non-linear transformation?

Calculating the coherence (sometimes called magnitude squared coherence) between two signals indicates the presence or lack thereof of a linear transformation between the two signals. Is there an ...
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1answer
730 views

Conversion from laplace transform to z-transform [closed]

I would like to know if $$ \text {Z-Transform ( } G(s)H(s) \text{ )} = \text {Z-Transform (}G(s) \text{)} \text { Z-Transform (} H(s) \text{) } = G(z)H(z) $$ where G(s), H(s) are the Laplace ...
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2answers
344 views

Combining two images

I am working with speckle noise reduction in ultrasound images. I have used wavelet transform for removing the noise by eliminating certain frequencies in order to eliminate any existing noise. Since ...
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0answers
148 views

Shifting of Shift-Invariant Wavelet Transforms

Main Question: Why would iterative wavelet/inverse-wavelet transforms cause a shift along the x-axis for undecimated (shift-invariant) wavelet transforms? I am attempting to remove backgrounds from ...
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4answers
212 views

physical meaning of fourier transform

I have a question regarding the fourier transform. If I plot the frequency against the fourier transform for a periodic signal and I get a peak, What is the physics behind it? I want to know the ...
4
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1answer
237 views

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 ...
2
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1answer
441 views

What is the definition of a noiselet?

I am reading about different integral transforms. Fourier transform being a subject I will soon take a class on. Looking at the wavelet transform there is one term that I do not understand, that is ...
4
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1answer
178 views

Motivation for using gabor transform instead of fourier transform

I am trying to understand the motivation for the above question for signal processing and image processing? Can anyone answer this question, or provide me with resources for this?
2
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1answer
194 views

Wavelet transform wavdec returns matrix of the wrong size

I have a question regarding the wavdecand dwt functions in MATLAB. I am using ...
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1answer
898 views

Hilbert-Huang Transform Implementation

I am looking for a implementation of Hilbert-Huang Transformation. Ideally, in Java, but any language with similar syntax would prove useful. Could someone point me to a specific implementation, ...
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1answer
58 views

Geometric Transformation in Gradient Domain Possible?

I work with images in gradient domain because I sometimes need to manipulate image gradients (i.e. Laplacian filter responses) rather than intensity values. However, I need to apply a geometric ...
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1answer
158 views

understanding bases and frames for Gabor transform

For the 2D discrete Gabor transform, why is it that we cannot use a set of orthonormal basis for its representation, instead we have to use frames for representing it?
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1answer
948 views

Ground plane estimation from a single image (was: confusion about homography and calibration camera parameters)

I'm new to this multiple view geometry issues and I'm a little bit lost, and some concept are not clear at all. I have a calibrated camera ( = I have distortion coefficents, field of view, and with ...