# 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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### 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. ...
788 views

### applicability of compressed sensing

From what I have heard, compressed sensing can only be utilized for a sparse signal. Is this correct? If that is the case, how can a sparse signal be distinguished from any bandlimited signal? Every ...
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### What does the normalization step of the Haar wavelet transform represent?

When you perform the Haar wavelet transform, you take the sums and differences, then at each stage, you multiply the entire signal by $\small\sqrt2$. When taking the inverse transform, you multiply ...
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### Filtering RANSAC Estimated Homographies

I am using RANSAC algorithm for homography estimation between pairs of images taken with cameras which do not have any translation between them (pure rotation and change of scale/zoom). It works well ...
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### 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 ...
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### How do I create a frequency vs time plot?

I'm a chemical engineer, not an EE, so this is a bit difficult. I'm trying to figure out how to take amplitude vs time data and transform it into frequency vs time. My first instinct is to slice my ...
381 views

### Wang Transformation

I'm essentially a math student working on algorithms for a chemistry problem involving rotational spectra, and I keep coming across references to Wang transformations but have been unable to track ...
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### 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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### 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) - ...
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 ...
942 views

### What do colored noises look like in the time domain?

I understand that the time domain representation of white noise looks like impulses. How do colored noises like brown, pink etc. look like when we perform an inverse Fourier Transform on them ? What ...
980 views

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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 ...
182 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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### 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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### 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 ...
501 views

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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### 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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### 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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### 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: "...
260 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 ...
133 views

### Understanding Walsh coefficients

I am working with Walsh coefficients. I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
109 views

### Global Transforms besides the DFT?

This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
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### FFT equivalent for generalized unitary transforms

The DFT has the FFT, Hadamard transform has the Fast Hadamard Transform and so do a number of other unitary transforms (operators). Is there or has there been an attempt at creating FFT style ...
664 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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### How to compute Discrete Cosine Transform

Can anyone please help me understand the 2D equation of DCT?I find it hard to understand it in terms of how to apply the equation. For example if I have an 8x8 image and I will apply 2D-DCT to every ...
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### 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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### Effects of interchanging sine terms with cosine terms

Suppose we have a real signal $x(t)$. Now, we know that $x(t)$ can be represented as a sum of sines and cosines. w be the angular frequency. If $a(\omega)$ be the coefficients of the cosine terms, ...