Questions tagged [math]

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78 views

Is it mathematically possible to compute Fourier transform without comparing the signal?

If I'm correct, Fourier transform lets me know the magnitude and phase of any given frequency in a signal. I have a sampled signal and I want to compute its Fourier transform (any frequency) without ...
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1answer
35 views

Help with Determinants [closed]

Okay so i understand the first det, which is why i got the correct solution. However for the second det, im not sure how to solve it since because of the different coefficents (0,2,4) and i tried of ...
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2answers
84 views

What is this theorem in this formula?

I just read a paper yesterday and there is confusion: I want to know what is reconstruction fidelity term and the theorem of changing the formula from upper to lower one. Is this theorm from ...
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0answers
42 views

Directional derivative [closed]

I know that D ⃗ v f = ∇ f ⋅ ⃗ v Dv→f=∇f⋅v→ is the directional derivative. My question is why must the vector ⃗ v v→ be a unit vector? I am sure there is an obvious answer, but my book doesn't really ...
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1answer
39 views

What is a “functional”? [closed]

I have read the wiki page (https://en.wikipedia.org/wiki/Functional_(mathematics) but it is not helping. I understand what a regular function is input > do something to that input > output. but ...
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2answers
104 views

Help in proper notations and mathematical formulation

For a given series, $S = \{-1,0,-2,1,etc\}$. The number of elements in $S$ is $N = 100$. Each $s_i$ belongs to a alphabet from a finite alphabet set $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
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1answer
80 views

How to prove this norm inequality?

$$ \left( \sum |z_i|^a \right)^b \geq \left( \sum |z_i|^b \right)^a, \quad \forall a\in [1,2], b\in [2,+\infty) $$ Actually this is equivalent to $$ \|z\|_a \geq \|z\|_b \quad \forall a\leq b $$
0
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1answer
142 views

Laplace transform of averaging operator

I am studying dc-dc converter now. I got a problem with Laplace transform of the averaging operator as in the image below. Can anyone help me derive the Laplace transform result $G_{av}(s)$ as in the ...
1
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1answer
53 views

Notation confusion — What is the correct operator for computation of the log-likelihood expression for complex valued data?

This question is an extension of another question of mine asked earlier here Help in understanding if the maximum likelhood estimation is working properly In that question the inputs were real valued....
2
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3answers
108 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 ...
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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 ...
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1answer
82 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/~...
3
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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 ...
2
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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?
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1answer
132 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 ...
5
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1answer
458 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 ...
-1
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1answer
284 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 ...
0
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2answers
322 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 ...
2
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1answer
83 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
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1answer
215 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 ...
2
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1answer
236 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 ...
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2answers
748 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
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1answer
86 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
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0answers
208 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: $$ = - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$ = - \int_{-\infty}^{0} e^{-at} e^{-st}dt$$...
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1answer
246 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 (...
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3answers
103 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 ...
0
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1answer
57 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 ...
3
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2answers
264 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] \...
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0answers
26 views

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

This is part formula of command-response model (Fujisaki Model): ...
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1answer
187 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?
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0answers
294 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 ...
3
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1answer
767 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 ...
0
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1answer
43 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. ...
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0answers
375 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 ...
8
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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.
2
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0answers
550 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
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 ...
1
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0answers
120 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) \...
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1answer
79 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 ...
2
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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 ...
3
votes
1answer
821 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&...
1
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1answer
2k views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
0
votes
1answer
477 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
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1answer
355 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
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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: ...