Questions tagged [notation]
19 questions
5
votes
1 answer
Why Cramér spectral representation and not DTFT for stochastic process
In a lot of time-series analysis references I find (written by mathematicians or statisticians rather than engineers), I find the following signal decomposition for a stochastic process, termed the "Cramér representation" (e.g. eqn 8.11 of this…
Robert L.
- 2,034
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4
votes
3 answers
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 impulse responses or system functions.
When I…
VMMF
- 932
- 1
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3
votes
1 answer
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 expected values of absolute…
Olli Niemitalo
- 12,226
- 1
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- 54
3
votes
3 answers
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 Transform, as in the input goes in the system and…
user3140379
- 55
- 7
3
votes
1 answer
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 pretty critical portions of the document, and…
Austen
- 153
- 4
2
votes
1 answer
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?
user137927
- 349
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- 16
2
votes
1 answer
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:
$$
x_{k} = Ax_{k–1} + Bu_{k – 1} + w_{k – 1}
$$
What does $\mathfrak{R}$ stand for?
andor kesselman
- 123
- 4
1
vote
0 answers
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, the first manipulation is
$SW = (SW + 1)/2$
this put my…
Lin
- 111
- 4
1
vote
1 answer
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 signals and signal processing. I know the…
user40095
1
vote
1 answer
Notations to Use in Formulating 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}
$\mathbf{h} = [h_0,h_1,\ldots,h_{p-1}]^\mathsf{T} \in \mathbb{R}^{1 \times p}$ of length $p$ which…
Srishti M
- 606
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0
votes
1 answer
What is the best concise mathematical notation for applying an IIR filter to a signal?
For denoting the application of an FIR filter with impulse response $\mathbf{k}$ to a signal $\mathbf{x}$ in time domain, we can use the convolution operation, i.e., $\mathbf{x}*\mathbf{k}$. What is the best concise way to denote the application of…
Reza
- 113
- 3
0
votes
2 answers
What is it called if a system is "in rest" until time $t=t_0$?
I am a mathematics student, and am quite new to the whole control and system theory (haven't heard any lectures). I currently work with dynamic systems, but do not know the correct words for every attribute, yet.
I would like to describe a system as…
Lukas
- 13
- 4
0
votes
0 answers
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 The term Krt controls reverb time, but what does the actual block do?
progressiveCavemen
- 143
- 9
0
votes
1 answer
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}\right]^{T} \in {\mathbb{C}}^{N} \\
{\tilde{\bf z}} &=…
Karn Watcharasupat
- 75
- 8
0
votes
1 answer
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 $E_{interested} = E(t)>C$ a proper notation?
Sajil C K
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