Building Acoustics

Oscillating systems 7

where crms denotes the RMS-value of the harmonic components. Using the complex form
of Equation (1.6) we get

22

2

rms 0

0

( ) 2 with 0.

kk

kk

kk

xxt X X X

=+∞ =+∞

=−∞ =

== =∑∑ = (1.12)

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Time (s)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

x(

t)

Figure 1.3 Periodic time function.

0 100 200 300 400 500

Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

|X

(f

)| (RMS)

Figure 1.4 Frequency amplitude spectrum of the time function in Figure 1.3.