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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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44 views

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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1k views

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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1answer
360 views

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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94 views

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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2answers
937 views

Image transformation where a curve becomes a straight line [closed]

Suppose that I have the green curve (image attached for visualization), values stored in a vector and I want to transform the image such that the curve becomes a straight horizontal line. So if the ...
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1answer
97 views

Critically Sampled Laplacian Pyramid from 2nd Generation Wavelet

I'd like to know if a technique I have in mind is already used and has a name I can look up, and whether it is likely to work and be useful! My aim is to produce a discrete wavelet transform that is ...
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1answer
1k views

Computing narrowband spectrograms using MATLAB [closed]

I'm having an assignment of computing narrowband spectrograms using MATLAB. And I totally have no idea about the code. Can someone help me writing the code and explaining what's going on to me. Lots ...
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1answer
400 views

Matrix form of STFT

IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...
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1answer
91 views

Geometric Transformation in Gradient Domain Possible?

I work with images in gradient domain because I sometimes need to manipulate image gradients (i.e. Laplacian filter responses) rather than intensity values. However, I need to apply a geometric ...
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1answer
300 views

understanding bases and frames for Gabor transform

For the 2D discrete Gabor transform, why is it that we cannot use a set of orthonormal basis for its representation, instead we have to use frames for representing it?
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4k views

Ground plane estimation from a single image (was: confusion about homography and calibration camera parameters)

I'm new to this multiple view geometry issues and I'm a little bit lost, and some concept are not clear at all. I have a calibrated camera ( = I have distortion coefficents, field of view, and with ...
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26 views

How to simulate Zoom, Pan, Tilt transformations? [closed]

Say we are looking at a football field from a broadcast view. To give us another tool, we also have a transform of that view to a topdown view. So our two views are like so: How would one simulate ...
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73 views

Any experiences for plotting a stationary wavelet transform?

I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides. There are very nice plots for CWTs, but does anyone know a technique for producing ...
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1answer
229 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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0answers
84 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
145 views

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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647 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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78 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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91 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
274 views

Mathematical advantages of the ZT, DTFT and DT?

I apologize if this question is too general to answer concretely, but I was hoping more to perhaps be pointed towards some resources that could help more extensively. Essentially, I have a Discrete-...
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1answer
146 views

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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1answer
503 views

Questions related to Laplace Transform

While studying Laplace transform, I also some questions which I want to understand: a) We used to say that Laplace transform include both real and imaginary part whereas in Fourier transform we ...
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1answer
703 views

How to extract IF (instantaneous frequency) from Discrete Hilbert Transform?

The continuous time Hilbert transform is $$\hat x(t) := x(t) + j\left( p.v. \left\{\frac{1}{t\pi} \ast x \right\} (t)\right)$$ where $$ \theta(t) = \tan^{-1}\left( \frac{ p.v. \left\{\frac{1}{t\pi} \...
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2answers
246 views

Complex numbers in a frequency domain of a 2D image [duplicate]

I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere. How are frequency domain and ...
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86 views

Connection with system analysis and laplace&Z transform

Laplace&Z transform is just frequency analysis of a system with a multiplication of decaying exponential. We analyse frequency with varying Laplace Exponential, which can be seen in the formula ...
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1answer
660 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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586 views

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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1answer
361 views

Fourier Transform of exponential

While solving Example 4.1 of Signals and Systems by Alan Oppenheim. Example 4.1 is: $$ x(t)=e^{-at}u(t), a>0$$ and the transform I get is: $$ X(j\omega)\frac{1}{a+j\omega}, a>0$$ The problem is ...
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994 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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2answers
96 views

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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1answer
748 views

Transformed Direct Form II filter: Z transform: reduce multiplications

In the diagram below there are three multiplication operations required to compute each filter output sample. I'd like to draw a block diagram of an equivalent filter but requiring fewer than three ...
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2answers
2k views

Getting the amplitude and phase of harmonics in C

I have a periodic series of 360 values. How can I use the fftw c libraries to get the amplitude and phase of the first, second, third and fourth harmonic? If I do this for N=360 ...
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1answer
81 views

How to achieve an arbitrary phase shift? [duplicate]

To help demonstrate why a time delay appears as a linear phase shift and not a constant phase shift I wanted to plot what a constant phase shift looks like. I have been looking at the Hilbert ...
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307 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
388 views

Discreteness and periodicity in Fourier transform

Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ...
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1answer
2k views

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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1answer
102 views

Why Z-transform is considered as separate transform?

The mathematical formula of the Laplace and Z transforms are same with just one difference. I.e. in the first we use $t$ for continuous-time signal and in the latter uses $n$ for discrete-time signal....
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1answer
107 views

Do signals with a Fourier transform with discontinuities or zero amplitude (in some frequencies) have Laplace transform?

I am reading a book on Laplace transform, and in the section on the convergence of Laplace transform for various signals the following theorem is stated, without any proof : If a signal's Fourier ...
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1answer
16k views

Conversion from laplace transform to z-transform [closed]

I would like to know if $$ \text {Z-Transform ( } G(s)H(s) \text{ )} = \text {Z-Transform (}G(s) \text{)} \text { Z-Transform (} H(s) \text{) } = G(z)H(z) $$ where G(s), H(s) are the Laplace ...
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1answer
44 views

Is it correct to assume that $(-1)^n = \cos(\pi n)$ while computing the DTFT of $(-1)^n$?

$\cos(\pi n)$ fluctuates between $-1$ and $1$ depending on the values of $n$, and it would be the same as computing it with an exponential but the problem is that I just get part of the right answer......
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2answers
91 views

My impulse response does not tend to zero

I am doing an IFFT of frequency response data achieved with Simulation tools. When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
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1answer
31 views

Time Setting of $z$ and Laplace Transforms

I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
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1answer
36 views

Region of Convergence

In attached image why does the ROC have these values for $$ X(z) = \frac{1}{1-\frac{1}{3}z^{-1}} - \frac{1}{1-2z^{-1}} ~~~~~,~~~~~ 1/3 < |z| < 2 $$ and for $$ Y(z) = \frac{5}{1-\frac{1}{3}z^...
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1answer
32 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
100 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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1answer
226 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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204 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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1answer
1k 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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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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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}\...