# 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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### How to do stretching Image distortion transformation

I have an assignment to transform an image like this: I have done with twirling, fisheye, bulge, but I'm having a hard time finding the right formulas for those effects. here is my code for twirling: ...
1 vote
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### How to use inverse 2D Fourier transform to reconstruct the original image?

I have managed to get the forward Fourier transform of an image to the frequency space like so: But I cannot for the life of me reconstruct the original image from the inverse Fourier transform of ...
13 views

### Are the sparsity of transform coefficients comparable when their frequency ranges are different?

I have obtained a graph-based Fourier transform from an optimization problem, and for evaluating the sparsity of transform coefficients, I was going to compare it with other transform coefficients ...
21 views

### How do you find the length of a constant q transform window in librosa?

I am working on a machine learning project to transcribe classical chamber music. I have a collection of audio files and for each time interval, I have data which tells me which notes are being played....
1 vote
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### How to objectively measure how "good" a time-frequency representation of music is?

I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal ...
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### Random projection with compressive sensing and hashing algorithms

I read that Random Projection matrices can be used in both Compressive Sensing and Locality Sensitive Hashing. I need simple explanation for the difference between applying Random Projection in both ...
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### FFT for Arbitrary time history

I have two Time-Speed histories one is real ( real measurements) the other is synthetically generated using formula. I need to compare both in the frequency domain using FFT given that: the time step ...
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### How to effectively stationarise non-periodic wave signals?

I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
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### simple explanation of rank transform and its relation to normal distribution

I tried to understand the rank transform, but I couldn't. The first step common to all histogram remapping techniques is the transformation of the pixel intensity values of the given image via the ...
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### How to alleviate the edging effect of the Hilbert transform?

I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
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### Fourier transform of an aperiodic discrete-time signal

I have a signal of the form $x^{*}(-n+2)$. To derive the signal's Fourier transform I use The following properties of DFT: $x^{*}(n)=X^{*}(-\omega)$ and $x(n-k) = e^{-j\omega k}X(\omega)$ so the ...
1 vote
I am studying a course in signalanalysis and have run into som trouble with a exercise. I am to dimension the circuit below in such a way that the DC-amplification is 1 and that the frequencies $\... • 53 0 votes 0 answers 20 views ### Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically with the signals in ROC? Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically? Are we supposed to manipulate our O/P by multiplying any signal from ... 0 votes 1 answer 54 views ### What is the meaning of spectral contamination in image processing? I resize the Multispectral image to perform IHS-to-RGB transformation. I used the Nearest Neigbour Interpolation method when resizing. While researching this issue, I saw that this is the best option ... • 53 3 votes 1 answer 70 views ### Can a linear reconstruction in compressive sensing perform well? I am trying to implement compressive sensing for grayscale 2D images, then reconstructing them using a multi-layer perceptron(MLP). It seems to perform well no matter how many layers I add or remove, ... -1 votes 1 answer 89 views ### Why does each node in the wavelet scattering transform split into multiple paths? Why does each node in the wavelet scattering transform split into multiple paths as in this figure from Deep Scattering Spectrum? I understand roughly what’s happening along a single path, but I don’... 3 votes 1 answer 137 views ### Why is incoherence important for compressive sensing? The literature on compressive sensing (CS) frequently notes that CS relies on two principles: sparsity and incoherence. While I understand why the signal of interest should be sparse in some domain ... • 31 1 vote 0 answers 24 views ### Application of the spherical Radon transform property in tomography Let function$f$be even and continuous on the unit sphere$S^n$. Let$R$-be a spherical Radon transform. There is a known property:$R(f^n)=f$whenever$f$=constant. What would this property mean in ... 4 votes 1 answer 2k views ### Scalograms in python I am reading this paper to learning basic concepts of dsp and I want to reproduce the following scalogram of a test signal (fig 4.2 of the paper): It has been produced from the discretization of the ... • 75 1 vote 2 answers 222 views ### Difficulty with a Fourier Transform What would be the best way to take the Fourier transform of $$f(t)\cdot \cos\big(\pi(t-1)\big)$$ I'm aware that when you take the Fourier Transform of$\cos(kt)you get two impulse at the location ... 2 votes 1 answer 269 views ### How can we prove the correctness of the integration property of the Laplace transform? I was going through an Electrical Engineering textbook for understanding the Laplace transform and came across the following proof for one of the properties of the Unilateral Laplace transform. ... • 155 4 votes 1 answer 176 views ### Phase shift of discrete cosine transform (DCT) The most common type of discrete cosine transform (DCT-II) is defined as \begin{align} X_k&=\sum_{n=0}^{N-1}x_n\cdot \cos\left(\frac{\pi}{N}\left(n+\frac{1}{2}\right)\cdot k\right)&\text{where ... 0 votes 1 answer 53 views ### multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function I already showed b item using the fact that it ish\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$I struggle a lot of hours trying to find the trick in item C. Can anyone help please ? • 177 1 vote 0 answers 112 views ### even symmetry of magnitude and odd symmetry of phase [closed] I'll appreciate it if any of you guys could help me with this question: Suppose that x(t) is a real signal, prove that the magnitude of its Fourier transform has even symmetry and its phase has odd ... 0 votes 2 answers 110 views ### How to test wavelet transforms? One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ... • 5,397 1 vote 3 answers 95 views ### Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree? MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ... • 73 3 votes 1 answer 270 views ### Understanding Parseval's Theorem with Discrete Wavelet Transform I have difficulty to understand the results I get with implementing Parseval's Theorem in Python to DWT. I have the good results getting the Energy with Fourier transform and the time series in python:... • 133 2 votes 2 answers 752 views ### 1D DCT matlab code I was writing MATLAB code to compute 1D DCT of sample y. On computing DCT for y=[0,1,2], code generates coefficient ... 0 votes 1 answer 41 views ### How to transform a signal to go through specific points? I have a 1d signal obtained using a Fourier based resample method (TDIFDZP) for which the resampled points don't necessarily go through the original samples. I want to transform the upsampled signal ... 1 vote 2 answers 159 views ### Question on N point DTFT - Fourier transform I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal. • 15 0 votes 1 answer 356 views ### What are the differences between the DWT and the MODWT? What are the differences between the DWT (Discrete Wavelet Transform), which is the most classical algorithm and the Maximum Overlap Discrete Wavelet Trasnform (MODWT)? Both these algorithm are ... • 363 0 votes 1 answer 67 views ### KLT for an ECG Signal I am currently searching for methods of feature extraction from an ECG signal and I've stumbled upon the Karhunen–Loeve Transform. I've read some papers and I think I get the basics but my question ... 4 votes 1 answer 135 views ### Downsampling, shifting, high pass and low pass filter commutativity strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself. ... • 183 1 vote 2 answers 241 views ### Question about Hilbert transform Hilbert transform of a function$g(t)$which is defined in time domain, would result in another function in time domain. Is there any other transformation like Hilbert that the results be in time ... • 69 1 vote 2 answers 465 views ### Is there an easy way to translate a Fourier transform table from angular frequency$\omega$to Hertz$f$? I have a table with transform operations, e.g. scaling: $$\tag{0} \label{0} x(at) \iff \frac{1}{a} X(\frac{\omega}{a})$$ or frequency shifting: \tag{1} ... 1 vote 0 answers 44 views ### Difference between these two Continuous Wavelet Transforms? I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ... • 5,397 0 votes 2 answers 457 views ### How to properly convert from dB back to amplitude I am new to signal processing. I have a signal that I want to convert to dB, process and then transform back. My understanding of the transformation to dB scale is$X_\mathrm{db} = 20 \cdot \mathrm{...
I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with \$n&...