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-1
votes
1answer
43 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 ...
1
vote
1answer
54 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 ...
0
votes
2answers
36 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 $x(2t)$ ...
0
votes
2answers
42 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 ...
3
votes
1answer
54 views

Derive chernoff bound for $\mathrm{erfc}(x)$

I'm trying to derive the Chernoff bound $\mathrm{erfc}(x) \le \exp(-x^2)$, by first showing: $$\mathrm{erfc}(x) = \frac{2}{\pi}\int_{0}^{\frac{\pi}{2}}\exp\left(-\frac{x^2}{\cos^2\theta}\right)d\...
0
votes
0answers
11 views

How to remove roots at z=1 by using pdiv function in scilab?

I'm trying to write a code for line spectral frequencies from prediction filter coefficient and I have two polynomials P1 and Q1 as arrays from which I have to remove the known roots at z=1 and z=-1(...
0
votes
1answer
45 views

Shape of Kaiser windowing function FFT response

I'm trying to determine the shape of the FFT response of a signal which had a kaiser windowing function applied to it. What I mean by this is if the shape is a normal bell curve or a Lorentzian ...
0
votes
2answers
78 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 ...
0
votes
1answer
29 views

How make L2 norm of all columns equal to sqrt(n)

I have an nxn matrix and I would like to have all columns/rows in the matrix to have L2 norm equal to sqrt(n). Is this possible?
0
votes
1answer
48 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 ...
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: $$ = - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$ = - \int_{-\infty}^{0} e^{-at} e^{-st}dt$$...
0
votes
1answer
40 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 (...
3
votes
3answers
177 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
40 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 ...
2
votes
1answer
84 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 ...
0
votes
1answer
93 views

How to calculate Gaussian kernel for a small pixel 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
36 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
74 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 ...
2
votes
3answers
408 views

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

I'm looking for books/resources out there that deal with, in detail, implementing mathematical functions - log/exponential/sine/cosine/inverse in fixed point arithmetic for DSP purposes. Looking for ...
3
votes
2answers
209 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
19 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
63 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
90 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 ...
5
votes
3answers
666 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 ...
3
votes
1answer
298 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 ...
1
vote
0answers
157 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
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. ...
5
votes
2answers
1k 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.
1
vote
1answer
164 views

L2-optimal 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 this problem. Basically, one ...
2
votes
0answers
203 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
250 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
75 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) \...
2
votes
0answers
149 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
626 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
74 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
444 views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
5
votes
1answer
337 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
259 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
221 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
82 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: ...