Questions tagged [math]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
2answers
1k views

Convolution by IIR filter, a case where circular convolution is allowed?

The question is, how to attain the frequency domain representation of any signal (which is finite, non-unit length) convolved with an IIR filter. The correct answer in my opinion is that there is in ...
1
vote
2answers
125 views

How to make the $\ell_2$ norm of all columns and rows of an $n \times n$ matrix equal to $\sqrt{n}$?

I have an $n \times n$ matrix and I would like its columns and rows to have $\ell_2$ norm equal to $\sqrt{n}$. Is this possible?
0
votes
1answer
109 views

Advantages of Splines in Compressed sensing

I am working in compressed sensing, basically in ECG reconstruction Normally we were using biorthogonal wavelets for reconstruction. Someone advised me to use exponential spline basis instead of ...
2
votes
0answers
348 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: $$ = - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$ = - \int_{-\infty}^{0} e^{-at} e^{-st}dt$$...
1
vote
1answer
338 views

How to efficiently calculate points of intersection of a straight line and a contour?

Ex. I have an image, let's say 100x100 pixels with some shape on it. And a set of straight lines that are passing through origin located at some point of image, for example origin located at point (...
10
votes
4answers
7k views

Looking for an arcsin algorithm

Does anyone have a simple algorithm for computing a reasonably accurate arcsine? By "simple" I mean some sort of polynomial that requires <= 5 multiplies per output sample. And by "reasonably ...
-1
votes
3answers
162 views

How to interpret the notation of a transfer function

Probably a stupid question, but I'm slowly making my way through Julius Smiths' filter book. The maths is slightly defeating me at points. This function $H(e^{j\omega t})$, why is it a function of ...
3
votes
1answer
351 views

SIFT: why it is invariant to affine tranlsation?

I am studying SIFT. I am a little confused in some of Lowe's algorithm. In order to have a descriptor invariant to translations like scaling, we must get rid of the scaling factor in LoG (Laplacian ...
4
votes
2answers
15k views

How to Calculate Gaussian Kernel for a Small Support Size?

How to calculate the values of Gaussian kernel? I think I understand the principle of it weighting the center pixel as the means, and those around it according to the $\sigma$ but what would each ...
0
votes
1answer
64 views

Getting a part of the invert of Si function

I'm working on an algorithmus that sould need the inverse of the SI function. since this last once isn't oviouse to calculate, I'm trying to get only the parobla part from the SI function, to be ...
0
votes
1answer
202 views

How to predict the cramped frequency of a digital filter based on an analogue frequency?

I have a second order analogue high pass transfer function (unity gain at infinity). It's magnitude response hits the -20 decibel line at a frequency of 5706 Hz (the corner frequency is 18000 and ...
8
votes
4answers
2k views

Books/resources for implementing various mathematical functions in fixed point arithmetic for DSP purposes

I'm looking for books or resources that cover the following in detail: implementing mathematical functions (e.g., logarithm, exponential, sine, cosine, inverse) in fixed point arithmetic for DSP ...
3
votes
2answers
286 views

Deriviation of the "Twiddle Sum" property

I can't seem to understand how to derive the "twiddle sum" property: $$\sum_{n=0}^{N-1}W_{N}^{kn}=N \ \delta[k\bmod N] $$ where $$ W_{N} \triangleq e^{\frac{j 2 \pi }{N}} $$ and $$ \delta[n] \...
0
votes
0answers
27 views

Why the formula below are critically-damped second-order linear systems?

This is part formula of command-response model (Fujisaki Model): ...
-1
votes
1answer
214 views

Accumulator with decay?

I am using an accumulator in the form of X + [Y-1], X plus the unit delay of the output. Is there an accumulator that follows this form, but will fall to 0 over time, similar to a differentiator?
0
votes
0answers
323 views

Problem calculating the average power of a vector?

I am calculating the average power of a vector. I would like to compare the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. Thank ...
9
votes
3answers
2k views

Functional analysis for signal processing engineers

It seems that the most advanced pure mathematics course most EE engineers take is Fourier analysis, and after that it's basically 'applied' courses. There's probably a good reason for this, but I'm ...
4
votes
1answer
911 views

How moving part pixel intensity values of video frames becomes dominant compared to stationary part intensities in reconstructed frames?

Hello everyone i want to do dynamic texture video sementation using the Fourier transform in MATLAB. I am applying 3-D fft on dynamic texture video frames (using matlab function 'fftn') and ...
6
votes
3answers
596 views

Upper Bound for the DFT (FFT) Coefficients of a Bounded Signal

I have a discrete signal $x[n]$ of length say $1024$, such that : $$-1 \leq x[n] \leq 1, \qquad \forall n$$ and let $y[k]$ be its DFT. Is there an upper bound for $|y[k]|$ ? (i.e. for the DFT of a ...
1
vote
0answers
386 views

How to understand energy function in thin plate splines?

guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
0
votes
1answer
44 views

Capacity computation in Costa sheme

I can not understand the following sentences, could you please anyone guide me ? "Comparing with the embedding in audio signals, the usable bandwidth is greatly reduced, from 22.05 kHz to 4 kHz. ...
6
votes
2answers
189 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in \mathbb{R}^{N \times N} $ which is a Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $, namely $ \hat{x} = \mathbb{E} \left[ x \mid z \right] $. Prove the ...
8
votes
2answers
4k views

What is the math behind median filter's noise reduction property?

I am interested in understanding the mathematical reason for why does applying a median filter on an image (or signal) result in reduction of noise.
4
votes
1answer
1k views

Design $ {L}_{2} $ Norm Optimal Infinite Impulse Response (IIR) Filters

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The MATLAB function firls() implements a solution to ...
2
votes
0answers
586 views

Tracking 2D positioning with IMU Sensor

I am using a miniature car and I want to estimate the position. We can not use GPS modules and most of the tracking systems that I saw, are using IMU sensor with the GPS module. In our car we are able ...
1
vote
1answer
391 views

Modeling Load Modulation

I'm trying to create a simple NFC/RFID software simulator and am having a hard time understanding the math fully. I know that NFC tags respond by load modulating the 13.56 MHz wave that the reader is ...
1
vote
0answers
145 views

Recovery of Bandlimited Signals after Companding and Low Pass Filter

Let $\Omega > 0$ and denote by $\mathcal{B}_\Omega$ the subspace of $L^2(\Bbb R)$ consisting of signals that are bandlimited to $(-\Omega, \Omega)$. Denote $\mathcal{L}_{\Omega} : L^2(\Bbb R) \...
4
votes
3answers
1k views

The Mathematical Relationship Between Derivative and Convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative ...
2
votes
0answers
173 views

How much is the chance for a pure mathematician (geometer) to get a postdoc in imaging if he switches fields after Ph.D. and apply for one? [closed]

Before I start my question, I should probably mention that this question might not be the right question to ask here, but I tried academiabeta, and stackoverflow, but without getting any to-the-point ...
3
votes
1answer
883 views

Determine Parameters of gaussian distribution to fit a certain Image-Filter

I'd like to know what the parameters for the two-dimensional gaussian distributions are, which create this (I think) quite common image-processing filter: $$ h_\sigma(x,y)= \left[ \matrix { 1&2&...
0
votes
1answer
124 views

A 3x3 image kernel takes 9 multiplications and 8 or 9 additions for each pixel?

I doubt because you have 9 multiplications and you are adding 9 numbers together, when using a 3x3 convolution matrix. Adding 9 numbers: 1+2+3+4+5+6+7+8+9 We are performing 8 additions as we repeat ...
1
vote
1answer
2k views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
5
votes
1answer
517 views

Derivation of fixed-point $\tt atan2$ with self-normalization

I'm trying to understand the maths behind this Fast fixed-point $\tt atan2$ calculation with self-normalization. In particular, equation $(2)$ for theta1 appears to ...
0
votes
1answer
967 views

Inverse Discrete Time Fourier Transform of a given Function using the definition

I would like to compute the Inverse Fourier Transform of a given function using the DTFT definition $$H(e^{jω})=\frac{1}{(2−e^{jω})(2−e^{−jω})}$$ But I have to use the definition of the DTFT $$H(e^{...
0
votes
1answer
398 views

Hidden Markov Model

I am trying to construct a Hidden Markov Model to predict the next state to go to. I am doing an example system, or, a test system that contains the following: Ok so the training I have used is: ...
1
vote
2answers
90 views

Showing processes as an Equation

I have developed an algorithm that counts the number of times a particular block (within a 2D block) crosses zero. Here's an example: ...

1 2
3