**Power/Alternative Energy**

# The RMS & Noise extension for Chart 4 (Macintosh)

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ADInstruments ApplicationNote

AEM28b 1 July 2001

The RMS & Noise extension for Chart 4

This application note explains how to use RMS & Noise, a Chart 4 for Macintosh extension that displays various

representations of a signal's changing power content.

Written by staff of ADInstruments.

Introduction

In many situations it is important to view the power

content of a signal. For example, the power in an EEG or

EMG burst may be more important than the actual shape

of the individual pulses. Other application areas include

the determination of the power in audio signals or in

noise pollution studies. Certain types of data reduction,

filtering, and signal envelope detection can be assisted

by calculation of the changing power content.

This document describes RMS & Noise v1.1 (or later

versions of 1.1 such as 1.1.1, 1.1.2 and so on) which is

compatible with Chart v4.0 or later for Macintosh. The

description may not apply in full to other versions of

RMS & Noise.

Installing the extension

Place the RMS&Noise(4) file in the Chart Extensions

folder in the Chart 4 folder. Ensure that you quit Chart

before installing or removing Chart extensions. The

extension will be loaded automatically when you start

Chart. When loaded, it adds `RMS...' and `Noise...'

items to the lower half of each Channel Function pop-up

menu (Figure 1). Choose one of these items to display

the corresponding dialog box (Figures 2 and 3).

Three different calculations are available: RMS from the

Root Mean Square dialog box, and SD and Variance

(SD2) from the Noise dialog box.

The calculations are similar in that they all involve a sum

of squared quantities (so that the final result is non-

negative), and are averaged over an interval (the `Time

Constant'). Details of the calculations are described later

(see Algorithms).

If the calculation is performed on-line (during

recording), a slightly time-delayed version of the

calculation is displayed to give a visual indication of the

final result. When you stop recording, the normal off-

line calculation is processed and displayed.

Time constant

RMS and Noise calculations are always performed over

a specified Time Constant (averaging time, or window

width). In a digitally sampled data system like PowerLab

this time is represented by a certain number, N, of data

points.

The calculation is often strongly affected by the value

you choose for the Time Constant (Figure 4). Longer

Time Constants give larger amplitude signals and good

smoothing of the results but lead to a poor effective time

resolution. Conversely, small values give better

resolution but results may appear noisier.

Figure 1. A Channel Function pop-

up menu with RMS... and Noise...

commands.

Figure 2. Root Mean

Square dialog box.

Figure 3. Noise

dialog box.

ADInstruments ApplicationNote

AEM28b 2 July 2001

In general you should try to choose a time constant

which represents at least 10 sampled points (the constant

may represent thousands of points if need be) but is short

compared to the time-scale of changes in signal power.

For example, in an EMG recording sampled at 1000 /s

(1 ms per point), 50 or 100 ms would be reasonable time

constants. In this case 50, or 100, points would be used

in the RMS or Noise calculation.

The RMS and Noise calculations can be used as an

alternative to the normal `integration' of

electromyographic and similar signals.

Moving or fixed windows?

A moving window replaces each data point by the RMS

or Noise value measured about this point (Figure 5;

channel 2). The calculation is then performed on the next

data point -- analogous to a sliding point average

calculation. This is numerically intensive and can

produce a slow result with large data files.

A fixed window (of time constant T) computes the RMS

or Noise value for a fixed time interval corresponding to

the time constant and replaces all data points in this

interval with the computed value. The calculation is then

performed on the next interval width T. The calculation

is fast, but results in a characteristic `cityscape'

appearance of the calculated result (Figure 5; channels 3

and 4).

End-effects

The behaviour of the two window types differs slightly

at the beginning and end of data blocks:

With a moving window, the calculation is made on the

first point, then the first two points, and so on, until the

calculation can be done on the number of points required

by the time constant. Thus at the beginning and at the

end of each data block there will be an interval (equal to

the time constant) where the RMS or Noise calculation

is only approximate. These intervals should usually be

disregarded.

A fixed window computes the RMS or Noise function

on intervals N points wide centred on points at N/2,

3N/2, 5N/2, and so on. The last interval is calculated on

number of points remaining in the data block, and

Figure 4.Time Constant pop-up menu and dialog box for

entering other values.

Figure 5.Voice signal recorded at 20k /s, with three traces calculated by RMS & Noise (all with 20 ms Time Constant).

RMS1 uses a moving window. RMS2 and Variance use a fixed window.The selection of raw data, RMS1 and RMS2 is shown

overlaid in the Zoom window (right).

ADInstruments ApplicationNote

AEM28b 3 July 2001

Document Number: AEM28b

Copyright ) ADInstruments Pty Ltd, 2001.

All rights reserved.

MacLab, PowerLab, and PowerChrom are

registered trademarks, and Chart and Scope

are trademarks, of ADInstruments. Other

trademarks are the properties of their

respective owners.

Contacts

International (Australia)

Tel: +61 (2) 9899 5455

Fax: +61 (2) 9899 5847

E-mail: [email protected]

Web: www.adinstruments.com

North America

Tel: +1 (888) 965 6040

Fax: +1 (866) 965 9293

E-mail: [email protected]

Europe

Tel: +44 (1424) 424 342

Fax: +44 (1424) 460 303

E-mail: [email protected]

Japan

Tel: +81 (3) 5820 7556

Fax: +81 (3) 3861 7022

E-mail: [email protected]

Asia

Tel: +86 (21) 5830 5639

Fax: +86 (21) 5830 5640

E-mail: [email protected]

www.ADInstruments.com

should generally be disregarded. On-line calculations use

the previous N points or, at the beginning of the data

block where fewer than N points are available, all the

previous points.

Algorithms

The algorithms used for RMS and Noise compute similar

quantities. An important difference is that the RMS

calculation relates to the power content of the total signal

(including the mean), while the Noise calculations ignore

the mean and are derived only from varying components

of the signal. In electrical terms, the mean corresponds to

the DC value, and varying components correspond to AC.

RMS

The RMS value at point n is given by:

where N is the number of data points in the time window,

Vi is the value of the raw signal at point i, and k takes the

value 0 for off-line analysis, or N for on-line analysis.

This approximates the trace which would be obtained

from a completely analogue system:

RMS n( )

1

N

---- V 2

i

i n N k+( ) 2/-=

n N k-( ) 2/+

=

RMS t( )

1

T

--- V 2

t td

t T 2/-

t T 2/+

=

where T is the time constant (time window) and

Vt is the value of the source signal at time t.

Noise

The SD (standard deviation) at point n is given by a

formula similar to that of RMS, but with the mean

subtracted:

where is the mean value of Vi over the window width.

Variance (SD2) is the square of the standard deviation,

given by:

Exclusions

Exclusions are a special type of comment that mark data

to be excluded from searches and calculations. The RMS

& Noise extension does not recognise exclusions: it

makes the same calculation whether or not exclusions

are present.

It is up to the user to treat results of such calculations

with care and reject them if necessary.

SD n( )

1

N

---- Vi V-( )

2

i n N k+( ) 2/-=

n N k-( ) 2/+

=

V

SD

2

n( )

1

N

---- Vi V-( )

2

i n N k+( ) 2/-=

n N k- 2/+

=

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