# 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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### Proof that there cannot be two non overlapping ROCs for LTI system Laplace Transformation [closed]

Given an LTI system where the X(S) s-plane looks like this: ------O-----------O------O-------O--------- P1 P2 P3 P4 (the os represent poles ...
28 views

### How to avoid the edge effects that may occur when applying the Hilbert transform (by mirroring)?

How to avoid the edge effects that may occur when applying the Hilbert transform (by mirroring) for image or image series signal? Code is appreciated (in python) please.
1 vote
69 views

### What's the meaning of the amount of frequency 0 in the Fourier Transform?

In the Fourier series, I knew that the coefficient $a_0$ represents the DC value, shifting the signal up and down by the amount. Then, what's the actual meaning of the amount of frequency $0$ in the ...
27 views

### Why DCT-III is not used as forward transform for image compression applications?

DCT-II is the most widely used type for image compression. This is due to its "Energy Compaction" property. According to this property, a good enough reconstruction of a natural image can be ...
1 vote
80 views

### Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?

Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
56 views

### Calculating transform for maximum decorrelation?

Suppose you have a set of $n$ sensors with overlapping sensitivities--like the cone cells of an animal retina, which is in fact the sort of system I am trying to model. Given the frequency-response ...
1 vote
22 views

### What are the modes of a transform basis?

So, I'm reading Steven Brunton's book, "Data Driven Science & Engineering", and I'm trying to understand what he means by mode in this following excerpt: Most natural signals, such as ...
575 views

### Real and imaginary parts of the Fourier transform of a pure cosine wave

My understanding of the Fourier transform is that the FT of a cosine wave should be non-zero in the real part and all zero in the imaginary part. This follows from the orthogonality of sine and cosine:...
1 vote
73 views

### Representation of Sampling Frequency in the Fast Fourier transform

I have 21600 data in the time domain. What Sampling frequency should I use? can someone explain the effect of showing the result by selecting different sapling frequencies? Cheers
31 views

### Implement a simple Continuous Wavelet Transform for specifics frequency

I have a question. I am worked with the Wavelet Transform, Continuous and Discrete. With the Discrete Wavelet I implemented a noise reduction in a signal, using Python library. Now i have a signal ...
92 views

### An new arranging of the discrete Sine transforms

Let $n$ be even and consider the non-normalized discrete Sine transform of type 5 which is $$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$ Let us denote $s_{-,l}$ by the $l^{th}$...
1 vote
155 views

1 vote
939 views

### 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 ... 1 vote
173 views

### 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 ...
68 views

### 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 ...
156 views

### 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 ...
406 views

### 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 ...
2k views

### 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 ...
327 views

### 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
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1 vote
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### 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 ...
1 vote
183 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. ...
1 vote
97 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 ...
448 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:...
1k 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 ...
82 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
220 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.
642 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 ...