Noise will contaminate the input and output signals in a test. The severity of this problem will vary widely from one case to another, but achieving an adequate signal-to-noise ratio is a general problem. The signal available for analysis, Z(t), will be the sum of the desired signal x(t) and the noise N(t):

Z(t) = x(t) + N(t)

The computed Fourier integral for a periodic signal will be

where Ck is the computed Fourier integral, Ck the true Fourier integral, n the number of periods of data analyzed, and T the period. The integral in Eq.

(4.9.2) is the error due to noise contamination. It has been shown (10) that this error is inversely proportional to the amplitude of the periodic signal and inversely proportional to the square root of the length (time duration) of the data record:

1 /(flvA) (4.9.3)

where a is the amplitude of the periodic input signal.