# Questions tagged [notation]

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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 ...
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 ...
64 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 ...
359 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 &...
78 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 ...
158 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 ...
1 vote
44 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, ...
80 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 ...
1 vote
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 ... 117 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 ...
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]^...
31 views

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 ...
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 $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,... 2 votes 1 answer 4k views ### Difference between 2$\pi f$and$\omega$in Fourier transform What is the difference when we use$e^{-j2\pi f}$and$e^{-j\omega n}$for Fourier transformation? 2 votes 1 answer 122 views ### What does ℜ symbol mean? I came across the symbol$\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 votes 1 answer 143 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 ... 0 votes 1 answer 93 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, ... 