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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 keep low frequencies in DCT

How can I keep a percentage r of the low frequencies of a Nx1 signal x using the Discrete Cosine Transform of it? Is it simply zeroing all but the first rN elements of DCT(x)?
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36 views

Nyquist Rate (Sampling Frequency) for $ {f}^{2} \left( x, y \right) $

We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$ Would it be correct to say that ...
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42 views

How can I calculate the Number of bins per octave?

I am trying to calculate the Constant Q Transform for Monophonic audio using Python. The Python has the library to calculate the CQT , the default value of num_bins_per_octave is 12. How would one ...
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62 views

Band-limited random signal with arbitrary distribution?

I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
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3k views

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. ...
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60 views

Extreme quantization of audio

I would like to take an audio sample and reduce it to a very limited set of numbers, with one value for amplitude and another for length. Example: I want to find the dimensions of the red boxes, ...
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49 views

Calculating fourier transform

I have just recently started doing fourier transforms and I'm a little confused. Can someone walk me through in detail how to calculate the Fourier transform of I'm not looking for answer, just an ...
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1answer
32 views

How is the ROC of a transform function determined?

Suppose I have $x[n]$ and $y[n]$, and I calculate their respective Z-transforms $X(z)$ and $Y(z)$ as well as their respective ROCs. Calculating $H(z)$ is as simple as calculating the quotient of $\...
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29 views

Denoising before or after Geometric Transform?

I am working on a image which needs denoising (bilateral filter) and a geometric transformation. I am not sure in which order these filters should be applied. Personally I think it is better to use ...
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1answer
42 views

Using the given identities, find the inverse DTFT

Using the given identities, $ a^nu[n]$ <===> $\frac{1}{(1-ae^{-jw})}$ $\delta[n-k]$ <===> $e^{-jwk}$ Find the inverse DTFT of, $ H(e^{jw}) = B \frac{e^{-jw}}{(1-ae^{-jw})}$ my attempt: $ ...
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40 views

Teager-Kaiser Energy Operator based Spectrogram

I plotted a normal spectrogram for 3 recordings (left), and their TEO (or TKEO) based spectrograms (right). I wanted to understand/read the differences between the left and right pictures. I do ...
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191 views

How to interpret Discrete Wavelet Transform Coefficients?

I want to extract features from DWT coefficients like Power Spectral Density, Max frequency, Min frequency etc. After taking DWT, we get coefficients D1, D2, A2 etc. But my question is, Are D1, D2, ...
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70 views

How many discrete fourier / cosine transform coefficients are needed to represent real signal in frequency domain?

I think I've gotten the answer correct but I need some clarification. The definition of the DFT is $$X[k] = \sum_{n=0}^{N-1}x[n] \, e^{-i2\pi nk/N},$$ and (one of) the definition of DCT is $$X[k] = ...
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52 views

Wavelet central frequency

What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet? Thanks.
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145 views

How to find transfer function of a logarithmic or power function?

I'm dealing with logarithmic system $\log_{10}(y(t)) = m \log_{10}(x(t)) + b$, and I need to find the transfer function, $Y(s)/X(s).$ What is the Laplace transformation of $\log_{10}(f(t))$? What I ...
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Wavelet Quality factor

I read in my lectures that a wavelet should have a constant quality factor Q but without any explanation. Can anyone please explain what do we mean by a quality factor. Thanks..
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1k views

Applying a wavelet transform to a 1D time series

I'm preprocessing a non-stationary financial time series as input for a machine learning algorithm, and I'm trying to reduce noise in my data. All the research I've looked at points towards wavelet ...
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77 views

Daubechies Transform Example on Integer Array

I'm very new to wavelet transforms and I've had difficulty in finding examples that do a good job illustrating the steps clearly enough for me to turn those steps into code. One of the best sources I'...
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1answer
84 views

What is the exact meaning of the output of the Discrete Fourier Transform

I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
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2answers
434 views

Transform RGB image to *look like* Infrared

Context: I'm trying to improve a pose estimation model so that it works better when my camera is in Infrared mode. Unfortunately I only have RGB images to train on. I realize that you can't convert ...
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1answer
479 views

3D world homography matrix calculation

I have a matrix in (x,y,z) coordinates and also i have a transformed version like (x_new,y_new,z_new). I need to calculate a transformation matrix that can transform (x,y,z) to (x_new,y_new,z_new). ...
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reconstruct skewed image from a moving vehicle?

Is it possible to reconstruct a image, which is streched, or blurred due to it being taken from while being in a moving vehicle? I mean, If I know the the velocity, and direction in which the vehicle ...
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1answer
40 views

Unclear inverse Z-transform of $G(z) = \frac{1-p}{z-p}$

In this paper on page 5 equation (10) is supposed to be the reverse z-transform of equation (5) on page 4. $$\frac{U(z)}{\bar{U}(z)} = G(z) = \frac{1-p}{z-p} \quad \leftrightarrow \quad u(k) = \bar{...
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876 views

Hilbert transform of sinusoid — apparent contradiction

The arrow "$\xrightarrow{\mathcal H}$" denotes a Hilbert transform: $$\cos(\omega t)\xrightarrow{\mathcal H} \sin(\omega t)$$ happiness. But $$\cos(\omega t) = \cos(-\omega t) \xrightarrow{\...
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1answer
111 views

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: "...
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1answer
103 views

Computational burden of EMD/Huang-Hilbert vs wavelet

I am working on an online application of signal processing and pattern recognition. It involves sampling the signal at 2 MS/s, extracting features and classifying. My classifier has pretty good ...
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1answer
138 views

Implementing the DWT

I have been given the task to implement the 5/3 CDF transform for image compression. Given that the impulse response for the low and high pass are: $h_1 = [-0.5, 1 ,-0.5]$ (High Pass) $h_2 = [-0....
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0answers
64 views

Calculating gyroscope data from accelerometer and attitude data

I am currently collecting accelerometer and attitude data using smartphone sensors. Data is collected at 100Hz over 2.5 seconds. Of which there are 250 accelerometer points and 250 points representing ...
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1answer
2k views

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 ...
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0answers
113 views

Implementing a ram-lak filter in javascript implementation of fast fourier transform?

Having a non-mathematical background I'm trying to understand how to implement filtering of data in the frequency domain as part of FFT. A javascript implementation of a discrete FFT is found here. ...
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1answer
835 views

What is the difference between Constant-Q Transform and Wavelet Transform and which is better

i have been seeking for a better Transform than STFT with high overleaping. The Transform should more suitble for the human auditory system. And i learned that there are at least 3 Methods i may use ...
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1answer
496 views

Conditions for which the Hilbert transform returns a correct phase

I'm quite new to signal analysis, and I'm currently trying to understand under which conditions a Hilbert transform can be used to compute the correct instantaneous phase and enveloppe of a given ...
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1answer
74 views

What is the general formula for radon back projection for a javascript implementation?

I'm aiming to implement a simulation of computed tomography back projection in javascript/HTML5 canvas. Trying to figure the correct approach for doing a back projections and I have been studying the ...
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1answer
34 views

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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1answer
32 views

HHT : Toning down noisy data

I've recently asked a question on stack overflow asking for different topics one can visit to solve the problem of wave re-construction. One of the recommended solutions was to implement the Hilbert-...
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1answer
48 views

Is there a special case in which wave atoms convert to curvelets?

I'm new to multi scale transformations. I was wondering if there is a special case where wave atom converts to curvelet transform? Can I use wave atom parameters to have curvelet properties?
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179 views

Non Periodic, Deterministic Power Signals

Any one know of work on non-periodic but deterministic power signals? Now one member in this class would be the quasi periodic signals. I wonder if there is a generalized Fourier analysis of non-...
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2answers
531 views

How to sketch the following discrete-time signal?

How to sketch the following discrete-time signal: \begin{gather*} x[(n-1)^2] \end{gather*} for the signal given below: Any help would be much appreciated.
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Significance of sequency ordering in Walsh-Hadamard matrices

So I've been doing some reading into Hadamard and related matrices (Slant, Walsh, , and have observed that there are three typical "orderings" of the rows based on various criterion. E.g. "Natural", "...
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3answers
1k views

Multilevel partial wavelet reconstruction with PyWavelets

I'm looking for a way to partially reconstruct branches of a wavelet decomposition, such that the sum would recreate the original signal. This could be achieved in MATLAB using: ...
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0answers
476 views

Hilbert Huang Transform: Negative value in instantaneous frequency

I'm working on Hilbert Huang Tranform and have a question on computation of instantaneous frequency. I'm using HHT toolbox by Patrick Flandrin for EMD and computing IF manually. Problem is that I am ...
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0answers
72 views

Values (amplitudes) of the CWT and their relationship to waveform amplitudes?

I'm coding up a scalogram in C++. Right now it calculates a single row of the CWT matrix and immediately maps it to a line of pixels. Trouble is my colouring scales with the values of the transform ...
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1answer
107 views

Transform coding gain of two channel Haar Wavelet transform (first stage)

Question My interpretation Work I'm attempting to do this in MATLAB. I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
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2answers
107 views

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 ...
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0answers
86 views

Intuitive interpretation of transform coding

I am currently studying source coding of waveform in a course of Information Theory and Coding. More precisely, I am trying to understand, both mathematically and intuitively, transform coding and its ...
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1answer
189 views

Complex Morlet coefficient

A complex Morlet wavelet looks like this: $$\psi(t) = C \cdot e^{i \omega t} \cdot e^{-t^2/2}$$ Here $\omega$ is the frequency and $C$ is some normalization constant. The first exponential ...
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1answer
457 views

Fourier Transform of a signal using direct integration and properties

Am trying to compute the Fourier Transform of a function using the properties of the Fourier Transform once and checking my answer using direct integration. My problem is that am not getting the same ...
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1answer
221 views

Does the use of a sparse basis in Compressed Sensing imply the need to have access to all the information beforehand?

According to literature, the CS framework operates on the knowledge that most natural signals are sparse in some domain given by a sparsifying transform operation $\Phi$ (Fourier, Haar, WHT, etc.). ...
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1answer
162 views

In 1D DCT, why is the input a vector?

The question is specific to this document: Image Compression. It is chapter 6 from book "A First Course in Applied Mathematics" by Jorge Rebaza. It is, a to the point explaination of DCT that is ...
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1answer
45 views

Laplace transform of $f\left(\frac{t - b}{a}\right)$

Consider the function $f\left(\frac{t - b}{a}\right)$. We want want to calculate its Laplace transform. There are two approaches: Firstly, let $g(t) = f\left(\frac ta\right)$. Then $\mathcal{L}\...