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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$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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22 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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21 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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27 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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22 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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24 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
37 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
89 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
46 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
72 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
61 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
65 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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65 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
101 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
64 views

Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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0answers
35 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
63 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
97 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
110 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
103 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
43 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
341 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
63 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
276 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 ...
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2answers
192 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
32 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
53 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 ...
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1answer
51 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
394 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
298 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
113 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
161 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 ...
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1answer
184 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 ...
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1answer
323 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 ...
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1answer
222 views

Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
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1answer
175 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?
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1answer
136 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
679 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
57 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
146 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
718 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 ...
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58 views

Complex Cepstral Transform and Audio Watermarking

I am doing research in audio watermarking and have come across the paper that uses the complex transform to embed the watermark in order to improve the robustness and inaudibility of the embedded ...
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1answer
283 views

Complex Cepstral Transform on Audio in MATLAB

Hello I am trying to computer the Complex Cepstral Transform of an audio signal. I am using wavread to get an array of data type double precision. However, when I ...
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0answers
277 views

3 Band Wavelet Transform In MATLAB

I am currently working on an audio watermarking project in MATLAB. I currently have a code I am using to construct a nxn 3 Band Wavelet Transform matrix. However, when I try to construct a matrix that ...
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1answer
280 views

Getting the amplitude and phase of harmonics in C

I have a periodic series of 360 values. How can I use the fftw c libraries to get the amplitude and phase of the first, second, third and fourth harmonic? If I do this for N=360 ...
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0answers
134 views

Harmonics on periodic functions [closed]

Ok I need to understand how some harmonic calculations work to apply some transforms. If I have a periodic functiion f(x). And I have the values of that function for several values of x (say x goes ...
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4answers
354 views

DFT-like transform using triangle waves instead of sin waves

We know that DFT (discrete Fourier transform) breaks down a signal into multiple frequencies of sine waves. Does there exist a transform that does the same thing, but for triangle waves? For my ...
3
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2answers
116 views

Question about harmonic calculations and other functionals for image analysis

I am implementing a method known as trace transform for image analysis. The algorithm extracts a lot of features of an image (in my case features pertained to texture) using a set of transforms on the ...
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55 views

Contourlet Transfrom for Image Compression

Before today I had no idea there is any Transform an such; i was only aware with DCT and Wavelet Transforms but today one of my teacher who is doing research on Image processing project had told me ...