# Questions tagged [math]

The tag has no usage guidance.

96 questions
Filter by
Sorted by
Tagged with
3answers
104 views

### Weighted Sum of Auto Correlation - Lower Bound

Given a vector $v$ with elements ${\left\{ {v}_{n} \right\}}_{n = - \infty}^{\infty}$ and denoting ${v}_{n}^{\left( k \right)} = {v}_{n - k}$, namely, a shifted vector by $k$ elements (Mind ...
1answer
81 views

### Unable to understand how the paper simplifies the covariance matrix - Kalman filter

The paper Convergence Analysis of the Unscented Kalman Filter for Filtering Noisy Chaotic Signals presents the convergence analysis of Unscented Kalman Filter download http://www.eie.polyu.edu.hk/~...
2answers
189 views

### What does the $n$ do in $1/(j \omega)^n$

I'm currently working through a research paper on beam forming. In this paper a magnitude compensation is introduced to compensate for frequency dependency. Due to other calculations low frequencies ...
1answer
144 views

### Independence of Noise at Each DFT Output

My math may be a little rusty, so I would like confirmation or correction or my calculations here. Given white noise samples, $x_i$, which are IID and zero-mean, and variance $\sigma^2_x$. I want to ...
1answer
74 views

### Hi, If I really want to focus on the mathematics of signal procesing, Should I do a Masters in EE or Math? [closed]

I'm an undergraduate electrical engineering student who has an interest in mathematics of signal processing. I want to be able to go to a graduate school where I can focus on more the mathematics and ...
1answer
45 views

### Splines and Gaussians [closed]

Higher-order splines all mostly look like Gaussians. I wonder how higher-order splines (from 3rd order onwards) and Gaussians differ. How can one differentiate them?
1answer
3k views

### Phase correlation vs. normalized cross-correlation

I asked this over at Mathematics Stack Exchange, but since this sort of lies on the border of the questions normally asked over there and the questions you see over here I'll ask it here as well. (As ...
1answer
271 views

### FFT: Linear to Logarithmic (TM4C, CMSIS & NeoPixels/ws2812)

I'm trying to perform an FFT using the CMSIS libraries. My FFT_Output[] provides 1024 bins of data as expected. The issue is that it's linearly spaced and I want to change it to a logarithmic scale ...
2answers
1k views

### State Estimation by steady state Kalman Filter

I am working with a discret Kalman filter on a System $x_{k+1}=A_k x_k+B_k u_k+\omega_k$ $y_k=C_k x_k+\upsilon_k$ $E[\omega_k\omega_k^T]=Q$ $E[\upsilon_k \upsilon_k^T]=R$ I have estimated the ...
2answers
121 views

### Wavelet filter coefficients from scaling filter coefficients

I am trying to develop a new type of wavelets and I found out a function that following a particular two scale relation. The function at a scale $t$ say $x(t)$ can be related in a finer scale $x(2t)$ ...
2answers
231 views

### Polar form of the Fourier transform of $\sin(t)$

I came across the Fourier transform of sin(t). It ends up being a purely imaginary (dirac delta) impulse pair. But when considering the frequency domain representation of a signal, we consider the ...
1answer
81 views

0answers
26 views

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

This is part formula of command-response model (Fujisaki Model)： ...
1answer
178 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?
0answers
286 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 ...
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 ...
1answer
734 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 ...
0answers
374 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 ...
1answer
42 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. ...
2answers
3k 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.
1answer
766 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 ...
0answers
542 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 ...
1answer
342 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 ...
0answers
119 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) \...
0answers
167 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 ...
1answer
811 views

1answer
346 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: ...
2answers
87 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: ...