The final step in the calculation is to normalize the synthetic random voltage into terms that can be programmed into the random equalization system used for recording the synthesized random tape. Since most random equalization systems are designed to handle the spectrum in terms of g^{2}/Hz rather than E/Hz expressed in dB (column
(I) of Figure
4-3) normalization factors must be derived to make this transformation.

The first step in the normalization calculation is to choose a 0 dB reference in g^{2}/Hz such that all the synthetic voltages
(when normalized) will fall within the dynamic range of the analyzer. This is
accomplished by assigning the highest synthetic random voltage (column (I) of
Figure
4-3) a g^{2}/ Hz value equal to 80% of the highest equalization range.

Example:

- Dynamic range of equalizer: .001 to 10.0
g
^{2}/Hz

- Highest synthetic random voltage: + 18.05 dB,

set + 18.05 dB = 80% of 10.0 g^{2}/Hz = 8.0
g^{2}/HZ (g_{x}) and solve for g_{0}(where dB = 10 log g_{x}/g_{0})

18.05 dB = 10 log 8.0 - 10 log g_{0}therefore g_{0} = .125 g^{2}/Hz (0 dB reference for normalization)

- To solve for g
_{x} (normalized spectral density) for any bandwidth filter (X) use the following equation:

dB_{x} = 10 log g_{x}/g_{0}

dB_{x} = 10 log g_{x}/.125

therefore g_{x} = .125 x 10 (normalization equation)

The normalization equation is then applied to the value
of the synthetic random voltage in each bandwidth (column (I) Figure
4-3) to determine the normalized spectral density - g^{2} /Hz which is tabulated in column (J), Figure
4-3 . An example utilizing the E/Hz dB value (column 1) for Filter No. 14 is detailed below:

Filter No. 14 synthetic random voltage: + 13.9 dB

normalization reference: 0 dB = 0.125
g^{2}/Hz

g_{x} (Filter No. 14) = 0.125 x 10

=
3.07 g^{2}/Hz