Questions tagged [notation]
The notation tag has no usage guidance.
21
questions
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What is the reason the Kronecker delta function is noted this way in DSP?
I'm trying to make sense of different notations used in DSP. This is sometimes quite hard since notation brackets like in x[n] are used both to denote a single value or a sequence.
In mathematics, the ...
- 443
2
votes
2
answers
221
views
Proper notation for frequency response between $H(\omega)$ and $H(j\omega)$
Short version: which notation is formally correct between $H(\omega)$ and $H(j\omega)$?
Disclaimer: I know that no one cares in the industry. I am asking out of curiosity and care for rigorous ...
- 85
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1
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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 ...
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votes
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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 &...
- 2,212
-1
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1
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Exponential Moving Average Function Notation
I'am trying to define an exponential moving average function denoted $EMA_{\alpha}(x_{n})$ where $\alpha$ is the smoothing coefficient and $x_{n}$ is the input signal. My first approach was to use the ...
- 225
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2
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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 ...
- 13
1
vote
0
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44
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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, ...
- 111
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0
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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 ...
1
vote
1
answer
141
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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 ...
user40095
3
votes
1
answer
117
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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 ...
- 13.5k
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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]^...
0
votes
1
answer
31
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)>...
- 149
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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 ...
- 1,078
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1
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129
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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 \...
- 616
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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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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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2
answers
109
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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 $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
- 849
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Difference between 2$\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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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:
$$
x_{k} = Ax_{k–1} + Bu_{k – 1} + w_{k – 1}
$$
...
- 123
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votes
1
answer
143
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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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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, ...
user15266