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Questions tagged [notation]

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Mathematical representation of a signal

I'm using a very simple signal to test some statistics. Let the period be $p = 2\pi$, I have two signal $SW = sawtooth(3 p)$ and $SQ = square(1.5 p)$ I do some manipulation in those two signal, ...
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0answers
28 views

What does KRT mean in this diagram?

I am working on building a reverb. This article explains how to build a reverb pretty well, but I do not understand what the KRT in the main diagram stands for. The article says ...
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1answer
57 views

What does this notation $g(x) = S\{\delta(t) \}(x)$ mean?

What does this notation mean $g(x) = S\{\delta(t) \}(x)$ mean, where $S$ is a "system", $\delta(t)$ is the impulse function and $g(x)$ the output function of the system? I am really not familiar with ...
3
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1answer
111 views

Ratio of expected values of squares of errors in power quantities, in dB

An amplitude quantity $a$ is estimated by two estimators $\hat a_1$ and $\hat a_2.$ The error of estimator $\hat a_2$ is compared to that of $\hat a_1$. One possible comparison is the ratio of ...
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1answer
40 views

Clarifying matrix notation from an ICA-CMN paper

In the paper I am referring (and here from citeseer), complex vectors $\mathbf{z}$ and matrix $\mathbf{M}$ were defined as follows \begin{align} {{\bf z}} &= \left[z_{1},z_{2},\ldots,z_{N}\...
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1answer
25 views

What would be the proper notation for denoting part of signal that satisfies a condition?

I have a signal $E(t)$ which start at $t=0$ and dies out overtime. What would be a proper notation to specify part of which is above a certain threshold (say for e.g. C)?. Is $E_{interested} = E(t)>...
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3answers
275 views

Why are numerator coefficients named $b$ and denominator coefficients named $a$?

This is not a technical question, it is rather a question about the implicit notation used in MATLAB and some digital signal processing books to refer to the numerator and denominator coefficients of ...
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1answer
101 views

Unable to understand what notations to use in formulating and example of Maximum likelihood estimation

The received noisy signal $y_n \in \mathbb{R}$ is expressed as: \begin{align} y_n = \mathbf{h}^\mathsf{T}\mathbf{u}_n + w_n. \tag{1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{p-1}]^\mathsf{T} \in \...
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3answers
828 views

What is the meaning of this notation?

I have seen this notation in the book Schaums-Outline a couple of times now and I can't quite understand it. I'd very much appreciate if someone explained what it means. I am thinking that it means ...
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1answer
420 views

Determining power spectral density from a sample

To start, I have absolutely no background in electrical engineering, I am a computer scientist by trade. I'm currently working on a project where I am attempting to code a function that uses the ...
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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
1k views

Difference between 2$\pi f$ and $\omega$ in Fourier transform

What is the difference when we use $e^{-j2\pi f}$ and $e^{-j\omega n}$ for Fourier transformation?
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1answer
77 views

What does ℜ symbol mean?

I came across the symbol $\mathfrak{R}$ in the Kalman introduction: Kalman Filter Intro $$ x\in \mathfrak{R}^m $$ It was used in this context: $$ x_{k} = Ax_{k–1} + Bu_{k – 1} + w_{k – 1} $$ ...
3
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1answer
108 views

Mysterious notation used in “BLIT” CCRMA paper

I'm working on a project involving synthesizing audio, which led me to a promising Stanford CCRMA paper on band-limited synthesis. However, this double-arrow notation keeps popping up throughout some ...
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1answer
72 views

Derivative Notation as a factor

In the figure below, from the book "Principles of Linear Systems and Signals - Lathi", the author uses the notation D to replace the Leibniz's notation $d/dt$, and after that he rewrites the equation, ...