Factor Analysis noise reduction

There are two primary difficulties in directly inverting equation (12.7). First, the system is usually underdetermined, which means there are more variables (e.g., wavelengths) than equations (e.g., number of calibration samples). Thus, direct inversion does not always yield a unique solution. Second, even if a pseudoinverse exists and results in a unique solution, the solution tends to be unstable because all measurements contain noise and error. That is, small variations in c or S can lead to large variations in b. Underdetermined and unstable models can be avoided by using data reduction methods, such as factor analysis, which reduce the dimensionality of the spectral data and much of the underlying noise within each spectrum. 

Analysis must compare desired noise levels in decibels to measured noise levels to determine the noise reduction, NR, required at each band center frequency. Analysis adds an adjustment factor of about 5 dB to each difference to ensure that higher noise levels do not render the enclosure ineffective. The transmission loss, TL, is the sum of the required reductions and the value resulting from the expression involving the room constant in Equation (23-15). 

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