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.

learn more… | top users | synonyms

0
votes
2answers
51 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 ...
0
votes
1answer
28 views

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" ...
0
votes
0answers
18 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 ...
0
votes
1answer
21 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 ...
0
votes
0answers
44 views

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 ...
5
votes
0answers
41 views

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. ...
0
votes
0answers
59 views

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 ...
0
votes
1answer
67 views

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 ...
0
votes
1answer
31 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 ...
-2
votes
1answer
43 views

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" ...
0
votes
1answer
25 views

Question about vanishing moments in wavelet tranforms

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 ...
0
votes
1answer
133 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 ...
0
votes
0answers
8 views

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 ...
2
votes
2answers
48 views

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 ...
1
vote
1answer
38 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 ...
1
vote
1answer
71 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 ...
0
votes
1answer
87 views

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?
1
vote
1answer
41 views

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: ...
0
votes
1answer
36 views

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 ...
0
votes
0answers
21 views

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 ...
0
votes
0answers
35 views

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 ...
3
votes
2answers
87 views

Multiplication property DTFT

I was truing to solve an example of DTFT which is following multiplication property. The problem is $$ a^n \sin(\omega_0 n) u[n]$$ we know that the definition of DTFT is $$ X(j \omega) = \sum _ ...
1
vote
1answer
28 views

Multiplier in digital signal processing?

whenever we start working on Discrete Cosine Transform(DCT), Loeffler algorithm a key role. Furthur if we approach hardware implementation of this algorithm, we find methods based on Distributed ...
3
votes
2answers
60 views

Question about z transform

After studying z transform from different books and literature on internet I want to ask few which makes me confuse. a) From the Discrete Time Fourier Transform we have drive equation for z ...
1
vote
1answer
24 views

Finding Laplace Transform without ROC

While studying Laplace Transform i found that region of convergence (ROC) is important because for some problems we have same Laplace Transform but different ROC helps us to take correct inverse ...
1
vote
1answer
34 views

Confusion in proof of Inverse Laplace Transform

For the proof of inverse Laplace transform, we change the integral from $\omega$ to $s$. I want to know the reason why we need to change the integral?
1
vote
0answers
36 views

Laplace Transform of $-e^{-at}u(-t)$

I have found a problem in applying Laplace Transform to $-e^{-at}u(-t)$ I am doing these steps: $$ = - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$ = - \int_{-\infty}^{0} e^{-at} ...
1
vote
2answers
47 views

Why we take Laplace Transform of functions which converged using Fourier Transform

There are several functions for which we know that Fourier Transform will exist but still we calculate its Laplace Transform. Can I know the reason why we need to take Laplace transform for which we ...
0
votes
1answer
54 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 ...
0
votes
1answer
60 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 ...
1
vote
1answer
40 views

Confusion in basics of Laplace Transform

I have few confusions while starting Laplace Transform. So far I have studied, Fourier series and Fourier Transform. The basic difference which I found from different books is Fourier Transform is ...
0
votes
0answers
33 views

Are Fractional Fourier transform applicable to non linear signals

I am aware that generally fourier analysis is applicable to linear signals from the literature papers. I wanted to know if fractional fourier transforms are also applicable to only linear signals ...
1
vote
2answers
89 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 ...
0
votes
1answer
57 views

Fourier Transform of image convoluting with kernel [closed]

edit: clarifying question. ...
0
votes
0answers
19 views

selection criteria for different projections

I need to know the percentage of height of human body parts, I have the following information that I used: my issue in selecting human which was not appeared straightforward (upright) with ...
1
vote
2answers
90 views

2D Haar Transform Computational Complexity

I want to learn the computational complexity of the 2D Discrete Haar (Wavelet) Transform (DHWT). The number of operations (divisions, summations etc.) is the main focus. I think there are many ...
1
vote
3answers
297 views

Why is a wavelet transform implemented as a filter bank?

The mother wavelet function $\psi(t)$ must satisfy the following: $$\int\limits_{-\infty}^{+\infty} \frac{|\psi(\omega)|^2}{\omega} d \omega < +\infty,$$ $$\psi ( \omega ) \bigg|_{ \omega =0} ...
0
votes
0answers
84 views

Difference between summation of motion components and IFFT?

I have a problem using the IFFT command. I want to see if i can go from the frequency domain to the time domain of a signal. I wanted to test this in two parts: 1) first creating a wave time ...
1
vote
2answers
68 views

Equation visualization of complex sinusoid function

I'm trying to learn Fourier Transform & Signal I can visualize how this expression $ A \sin(2 \pi f t)$ could turn into that curvy sinusoidal signal. But i couldn't visualize how $F(\nu)e^{2 \pi ...
1
vote
1answer
163 views

Fourier transform 4 times = original function (from Bracewell book)

I was glancing through "The Fourier Transform & Its Applications" by Ronald Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the FT of a function 4 ...
0
votes
0answers
92 views

Generating Wavelet family matrixes

We have unnormalized Haar matrix which, is for example, H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1] After normalizing it, we use for haar transform. I know how to ...
0
votes
0answers
22 views

Transformation validation

I am trying to see the validity of my geometric transformation, by imposing a point I got from a tracker in the original image and superimposing it on the image after the transformations. The point ...
0
votes
1answer
55 views

Audio phase shift using Hartley Transform

I want to shift the response phase of an audio signal (float array, length N, value range -1..1). I'm about using Fast Hartley Transform to transform it to the frequency-domain, process phase shift, ...
0
votes
1answer
52 views

STFT multiplied with Gaussian window vs STFT multiplied by rectangular window

I am currently analysing my signal by looking at its spectrogram to determine the sinusoidal frequency content at the local sections of my signal overtime. I can do my spectrogram in 2 ways: ...
1
vote
3answers
409 views

How condition for existence of Fourier transform is valid?

The condition for Discrete time Fourier transform to exist for function $f(n)$ is given as $$\sum_{-\infty}^\infty |f(n)| < \infty.$$ In case of continuous Fourier transform the difference is ...
5
votes
2answers
52 views

Finding filaments in high dimensional space

I have unit vectors in a high-dimensional space (~300) that are non-uniformly distributed over this hypersphere. There is physical meaning when the vectors are clustered together, but I'm ...
1
vote
1answer
122 views

Whether Fourier transform formula be considered as Convolution or Correlation?

The expression for Fourier transform is given as $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^{-j \omega t} \ dt \tag{1}$$ Now, let one function be $f(x)$ and other be $e^{j\omega t}$ ...
0
votes
1answer
56 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 ...
0
votes
1answer
38 views

Help with Hankel Tranform filters

I found a filter for Hankel Transform . As far as i understand this is effectively used as an approximation for J0(x) and J1(x) . But how will the change in input affect these filter terms (eg J0(r) ...
1
vote
0answers
31 views

Is affine the right transformation for coordinate change?

I have a video which was used in a tracking program. In that program the object being tracked receives per frame X,Y coordinates which are not the same as in the my video. I have a few coordinates ...