Consecutive signals

Consecutive signals (British: Continuous signal) or the consecutive time signals (British: Continuous-time signal) are values to change expressed as a function of the domains (usually time) of the actual numbers (signal). The functions of that time may not continue.

When it is limited, the domain that consecutive signals are defined may not be so either, and the function representation from a domain to the value of the signal exists. In conjunction with a law of the density of real number, the continuity of the variable means that the value of the signal is found about any any point in time at time.

The model example of the endlessly sustained signal is as follows.

${\displaystyle f(t)=\sin(t),\quad t\in \mathbb {R}}$

The limited sustained printing block of this signal is as follows.

${\displaystyle f(t)=\sin(t),\quad t\in [-\pi ,\pi]}$ Other than it ${\displaystyle f(t)=0}$

The price of the limited (or infinite) sustained signal may not be limited. For example,

${\displaystyle f(t)={\frac {1}{t}},\quad t\in [0,1]}$ Other than it ${\displaystyle f(t)=0}$

The という limited sustained signal ${\displaystyle t=0\,}$ If のときに is infinite, it becomes.

I suppose that the consecutive signals are always a limited price in many fields and am easy to treat the with the, for example, physical signal. Depending on a use, I may permit an infinite singular point as far as it is integrability in any limited section (e.g.${\displaystyle t^{-1}}$ I cannot integrate the という signal,${\displaystyle t^{-2}}$ Then) which I can integrate.

Generally the analog signal is continuation. When it becomes the disintegration signal when I become a specimen from there and quantizes it from there, a digital code used by digital code processing is provided.

I may define the consecutive signals about an independent variable except the time. For example, I treat the consecutive signals which assume two dimensions space an independent variable by the image processing.

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This article is taken from the Japanese Wikipedia Consecutive signals

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