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Questions tagged [notation]

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Why is sampling frequency/rate typically abbreviated Fs and not Sf in English?

This is not a technical question, it is rather a question about the implicit notation used in MATLAB and multiple digital signal processing books to refer to sampling frequency/sampling rate. Why is ...
VMMF's user avatar
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3 votes
1 answer
256 views

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 ...
mins's user avatar
  • 463
2 votes
2 answers
435 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 ...
chuchvara's user avatar
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1 answer
74 views

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 ...
Reza's user avatar
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5 votes
1 answer
415 views

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 &...
Robert L.'s user avatar
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-1 votes
1 answer
86 views

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 ...
alexgrover's user avatar
0 votes
2 answers
184 views

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 ...
Lukas's user avatar
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1 vote
0 answers
45 views

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, ...
Lin's user avatar
  • 111
0 votes
0 answers
90 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 ...
progressiveCavemen's user avatar
1 vote
1 answer
141 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 ...
user avatar
3 votes
1 answer
118 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 ...
Olli Niemitalo's user avatar
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1 answer
53 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}\right]^...
Karn Watcharasupat's user avatar
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)>...
Sajil C K's user avatar
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5 votes
3 answers
874 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 ...
VMMF's user avatar
  • 1,142
1 vote
1 answer
134 views

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 \...
Srishti M's user avatar
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3 votes
3 answers
1k 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 ...
user3140379's user avatar
0 votes
1 answer
721 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 ...
Ryan's user avatar
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0 votes
2 answers
109 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,...
Ria George's user avatar
2 votes
1 answer
5k 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?
user137927's user avatar
2 votes
1 answer
124 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: $$ x_{k} = Ax_{k–1} + Bu_{k – 1} + w_{k – 1} $$ ...
andor kesselman's user avatar
3 votes
1 answer
147 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 ...
Austen's user avatar
  • 153
0 votes
1 answer
95 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, ...
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