# 1. Signal related concepts

• Signal: In the category of signal and system, signal is described as a function with time as the only independent variable. Generally, continuous signal is used for x(t)representation, and discrete signal is used for x[n]representation.
• Signal power and energy: The physical quantity that describes the signal energy, as shown in the following table. When the range tends to positive infinity and negative infinity, respectively, it is an infinite range of energy.

definition

formula

The energy of the signal in a certain time range

$\int^{T1}_{T2} x(t) 2dt$ (continuous), $\sum\limits{T1}_{n=T2} x[n] ^2$ (discrete)

The power of the signal in a certain time range

$\frac{1}{T1-T2}\int^{T1}_{T2} x(t) 2dt$ (continuous), $\frac{1}{T1-T2}\sum\limits{T1}_{n=T2} x[n] ^2$ (discrete)

• Independent variable transformation: for a signal

Perform a linear transformation of the independent variable

, The different transformation combinations are shown in the following table:

Transform

Parameter transformation

For example

Time shift

Time movement, when, the signal moves to the right side of the time axis, and vice versa

Reverse

Time reversal, the signal is reversed in time, similar to tape rewinding

Scaling

The time scale is stretched and time is accelerated, similar to the acceleration of music playback, and vice versa

• Periodic signal: For continuous signal, it satisfies any t

The signal of is a periodic signal, otherwise it is a non-periodic signal, and the smallest T is the fundamental wave period; for discrete signals, any n is satisfied

The signal of is a periodic signal, otherwise it is a non-periodic signal, and the smallest N is the fundamental period.

• Odd signal and even signal: The concept of odd signal and even signal is as follows, any signal

Can be decomposed into an odd signal

And an even signal

The sum

concept

definition

Odd signal

For any t or n, satisfy or

Even signal

For any t or n, satisfy or

## 1.2. Step signal and impulse signal

Reference: https://cloud.tencent.com/developer/article/1704650 network study notes 2-physical layer basics (signal and system) (to be continued)-Cloud + Community-Tencent Cloud