# Tagged Questions

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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### $\mathcal{Z}$-transform of $\frac{1}{n^2}$

This is a Question asked in IISC ( Indian Institute of Science,Bangalore,India) interview for MS admission. What is the $\mathcal{Z}$-transform of $\dfrac 1{n^2}$ ?
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### Biquad coefficients using Magnitude (or Phase) Invariance Mapping Method

I'm trying MIM (Magnitude Invariance Method) and PIM (Phase Inveriance Method) for to improve biquad LPF response at low sampling rates. I'm not sure if these methods can be used for this purpose so I'...
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### correcting wobbling motion in sinogram

I have measured some sinograms of a specific sample. However, there is some wobbling motion that disturbes the resulting images. Since the red upper and lower lines (indicated with black arrows) are ...
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### involutory transformations - why are they not so much used in signal processing? [closed]

We generally prefer orthogonal transformations/matrices in signal processing as the transpose of the matrix is the inverse and you do not need to find inverse transform separately. But involutory ...
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### How can the given two equations of linear canonical transform equate?

I am new to linear canonical transform and its uses in signal processing, my doubt arises from two different equations that i got from two different sources for linear canonical transform one is from ...
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### What transformation (or similarity metric) is rotation, shift, and scale invariant?

I have an algorithm to to detect copy-move forgeries in images. I used block matching to detect regions of an image that were forged with copy-move forgery and highlighted the alleged areas. For block ...
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### One-bit depth audio

I have a music player which is only able to play sound with one a bit-depth of one. I can produce this by taking a song and simply boosting the signal $+100\textrm{ dB}$. Is there another approach ...
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### Synthetic sounds to describe motion in 3d or 100d

Watch a butterfly flitting about, or an optimizer chugging along in 3d or 100d -- a sequence of points $X_1 \ X_2 \ X_3\ \ldots$ How could one generate synthetic sounds that convey moving fast or ...
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### DWT architecture using filter bank

I am studying this paper. In one of the figures in the paper (Fig 5.b and Fig 5.c) DWT architecture is given using db2 and filter bank. I don't understand how Lo_D and Hi_D have size half of input ...
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### How to calculate Fourier's coefficients of a $T$-periodic function with Scilab?

I have a vector of a size $N>1$ (it represents the values of a $T$-periodic function on a interval). I want to calculate its Fourier's coefficients with the fft, ...
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### How would Fourier and Cosine Transforms responds to summation of cosines with same frequency but different phases?

For example, if I have two signals, $\cos(2\pi ft+\frac\pi4)+\cos(2\pi ft+\frac\pi3)$, what would be different in both transforms (Fourier and cosine) how would the spectrum changes? And What would ...
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### Useful natural “Hilbert-like” $n$-uples and $n$-fold "analytic signals

If $\mathcal{H}$ denotes the Hilbert transform, the analytic signal of a signal $x(t)$ is $$x_a(t) = x(t) +\imath \mathcal{H}(x(t))\,.$$ The real and imaginary parts form Hilbert pairs. Are there ...
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### How can this equation hold $$\sum_{m=0}^{N-1} \sum_{n=0}^{N-1} |u(m,n)|^2 = \sum_{k=0}^{N-1}\sum_{l=0}^{N-1} |v(k,l)|^2$$?

I am trying to learn digital Image processing by myself and now stuck at a problem in the two dimensional unitary transformations. It states that let $U$ be the input image and $V$ be the transformed ...
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### Complex Conjugate Sinusoids in Forward DFT

I hope this isn't such a dumb question, but I'm finally getting to grips with the inner workings of the DFT. What I'm having trouble understanding is why the basis complex sinusoids in the "forward" ...
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### Accelerometer - coordinate system transformation

I'm getting some accelerometer readings from an Android phone, but it comes in on the phone's coordinate system. I want to apply a transformation to put the acceleration in the world coordinate system ...
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### Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
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### Fourier transform on Scilab of a Gaussian function

I am trying to do a fourier transform on Scilab, of the Gaussian function $y(x)=\exp(-\frac{x²}{2})$, by using the fft command. So I plotted the graph of ...
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### Expanding piecewise polynomial using Daubechies wavelet

What is the best Daubechies wavelet (i.e. the number of vanishing moment) to expand a signal $\boldsymbol{x} \in \mathbb{R}^n$? $\boldsymbol{x}$ consists of $m$ pieces of polynomial with $d$ degree. ...
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### s_to_z (Pupalaikis)

Paper: Bilinear Transformation Made Easy - http://documents.mx/documents/easybilinearpdf.html Example of implementation - http://codepad.org/u3tvKn0S I get the same output for Butterworth lp example ...
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### Discrete wavelet transform

I am unable to understand the discrete wavelet transform on images. I followed Robi Polikar's tutorial and got a brief idea about the theory. But I'm unable to understand w.r.t images. Using Matlab's ...
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### Inverse Fourier Transform problem

One of my tutorial questions for communication systems asks me to find the time function $x(t)$ which has the Continuous-Time Fourier Transform: $$X(\omega) = \frac{3}{(1+j\omega)(2-j\omega)}$$ So far ...
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### Find $X_s(f)$ of a sampled continuous signal

I've been trying to find the transform of the following signal, but have not been successful, any help would be greatly appreciated: Find $X_s(f)$ of the following signal the "mathematical DAC" ...
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### Question about vanishing moments in wavelet transforms

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...