Matlab: Vector normalization to a new peak or RMS value

The following example shows how to normalize a vector to a new peak or RMS (root-mean-square) value. The rms function from the digital signal processing toolbox is used. For details about the calculations for RMS, see a previous article.

RMS = √(∑x_i²/n)

Vector a:

>> a = [1 3 10 2 5 7 8 17 14]

a =

     1     3    10     2     5     7     8    17    14

Normalize to a new peak:

>> target_peak = 15

target_peak =

    15

>> a_newpeak = a*target_peak/max(a)

a_newpeak =

    0.8824    2.6471    8.8235    1.7647    4.4118    6.1765    7.0588   15.0000   12.3529

Normalize to a new RMS value:

>> target_rms = 10

target_rms =

    10

>> a_newrms = a*target_rms/rms(a)

a_newrms =

    1.1051    3.3152   11.0506    2.2101    5.5253    7.7354    8.8405   18.7861   15.4709

Check the RMS value:

>> rms(a_newrms)

ans =

    10

References:

Root mean square (Wikipedia)/平方平均數(維基百科)

rms: Root-mean-square level (MathWorks)

Matlab: Min, Max, Mean, Square, Mean-Square, RMS (StudyEECC blog)

Matlab: Min, Max, Mean, Square, Mean-Square, RMS

The following example shows how to get the minimum, maximum, average/mean and RMS (root-mean-square) values from a vector.

RMS = √(∑x_i²/n)

>> a = [1 3 10 2 5 7 8 17 14]

a =

     1     3    10     2     5     7     8    17    14

>> b = min(a)

b =

     1

>> c = max(a)

c =

    17

>> d = mean(a)

d =

    7.4444

>> e = a.^2

e =

     1     9   100     4    25    49    64   289   196

>> f = mean(e)

f =


   81.8889

>> g = sqrt(f)

g =


    9.0492

where

b = minimum
c = maximum
d = mean/average
e = square
f = mean-square
g = root-mean-square (RMS)

The RMS value can also be worked out in a straight-forward command:

>> a_rms = sqrt(sum(a.^2)/length(a))

a_rms =

    9.0492

Or use rms in the digital signal processing toolbox:

>> a_rms_toolbox = rms(a)

a_rms_toolbox =

    9.0492

Reference:

Root mean square (Wikipedia)/平方平均數(維基百科)

rms: Root-mean-square level (MathWorks)

Matlab: Vector normalization to a new peak or RMS value (StudyEECC blog)