# Significance of RMS (Root Mean Square) value

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Loading... Root Mean Square (RMS) value is the most important parameter that signifies the $$size \; of \; a \;signal$$.

### Defining the term “size”:

In signal processing, a signal is viewed as a function of time. The term “size of a signal” is used to represent “strength of the signal”. It is crucial to know the “size” of a signal used in a certain application. For example, we may be interested to know the amount of electricity needed to power a LCD monitor as opposed to a CRT monitor. Both of these applications are different and have different tolerances. Thus the amount of electricity driving these devices will also be different.

A given signal’s size can be measured in many ways. Some of them are,

• Total energy
• Square root of total energy
• Integral absolute value
• Maximum or peak absolute value
• Root Mean Square (RMS) value
• Average Absolute (AA) value

### RMS value

RMS value of a signal ($$x(t)$$) is calculated as the square root of average of squared value of the signal, mathematically represented as $$E_{RMS} = \sqrt{ \frac{1}{T} \int_{0}^{T} x(t)^2 dt}$$ For a signal represented as $$N$$ discrete sampled values – $$[x_0,x_1,\cdots,x_{N-1}]$$, the RMS value is given as $$E_{RMS} = \sqrt{\frac{x_0^2+x_1^2+\cdots+x_{N-1}^2}{N}}$$ If the signal can be represented in Frequency domain as $$X(f)$$, then as a result of Parseval’s theorem, the RMS value can be calculated as $$E_{RMS} = \sqrt{\sum \left| \frac{X(f)}{N} \right|^2}$$

### Significance of RMS value

•  One of the most important parameter that is used to describe the strength of an Alternating Current (AC)
• RMS value of an AC voltage/current is equivalent to the DC voltage/current that produces the same heating effect when applied across an identical resistor. Hence, it is also a measure of energy content in a given signal.
• In statistics, for any zero-mean random stationary signal, the RMS value is same as the standard deviation of the signal. Example : $$Delay \; spread$$ of a multipath channel is often calculated as the RMS value of the $$Power \; Delay \; Profile$$ (PDP)
• When two uncorrelated (or orthogonal ) signals are added together, such as noise from two independent sources, the RMS value of their sum is equal to the square-root of sum of the square of their individual RMS values.