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Quantifying Signals – Peak, Peak-to-Peak, &

RMS metrics 

By John Mathey 

 – February 26, 2013Posted in: featured, signal processing 

Anytime you measure something which is changing with time, there are multiple waysto quantify the signal. For the purpose of this discussion, we will be talking about how

to describe the signal in the time domain.

There are several ways to describe what the time signal is doing. Perhaps the easiest

to understand are the Peak and the Peak-to-Peak measures of the signal. These are quite easily

understood by looking at the graphical representation of how the signal changes with respect to

time. For this purpose, we look at the graphical representation of a simple sinusoid signal.

Figure 1: A simple sinusoid

 Note that this is a very well behaved and repetitive signal so it is easy to determine the actual

values of the signal. It is readily seen that the absolute maximum value (Peak value) of the signal

over the measured time is 1.00 Volts (1.00 Vp) and the absolute minimum value of the signal isseen as -1.00 Volts, so the Peak-to-Peak value is 2.00 Volts (2.00 Vpp). In the case of this signal

the Mean value is 0 (zero) Volts, but this does not always have to be the case, as is seen in the

following example..

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Figure 2: Sinusoid with mean of 0.5

This is the same signal as before, but now it has an offset but with a mean value of 0.5 Volts, The

absolute maximum value is 1.50 Volts (1.5 Vp), and the absolute minimum value is -0.50 Volts,so the Peak-to-Peak value is still 2.00 Vpp.

Another measure of signals is called RMS which means root-mean-square of the signal, alsoknown as the quadratic mean. It is a statistical measure of the magnitude of a varying quantity.

This measure gives additional information about the signal, namely the “power” of the signal. Inmore practical terms the RMS Voltage of a time varying signal is the equivalent dc Voltage

which yields the same power.

This metric is calculated just as the name implies (RMS means the “root” of the “mean” of the

“square” of the values of the signal). First the value of each point of the signal is squared, then

these values are averaged over time, and then once this single number is calculated, the square

root of this number is the RMS value of the signal. For discrete data points, this ismathematically calculated as:

where is the sequential number of steps in time.

For continuous functions

Where is the time over which the average is taken.

Another metric sometimes used to quantify a signal, although not as frequently, is the average.This is calculated in similar way to how the RMS is calculated, but in this case the signal values

are not squared before averaging and the final number is not square rooted.

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Looking at examples of how the Peak and Peak-to-Peak values are determined and how the RMS

values are calculated shows that the Peak measurements are instantaneous measures whereas the

RMS values are average measures. Note that all of the metrics described for quantifying a time

signal are totally independent of the period or frequency content of the signal. These calculationscan be applied to any time varying signal no matter how complex.

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 Tags: dc voltage, magnitude,  peak to peak ,  peak value, rms, rms voltage, root mean square, 

statistical measure, time domain, time signal, vpp 

About John Mathey

John Mathey graduated with a MS degree from the University of Toledo in 1972. John has over 

35 years of experience with instrumentation, measurement, and analysis. Twenty-five of thoseyears were spent at Ford Motor Company solving and providing training for vehicle noise,

vibration, and harshness (NVH) issues. He is now a technical specialist at Prosig USA, Inc.

where he provides technical support to Prosig customers in the U.S.A.