Method and apparatus for high-resolution spectral analysis

Claim 2

A system as defined in claim 2 wherein said computer provideS compensation for variations in gain in the production of said first and second product signals by normalizing said sampled data employed in computing said correlation functions.

Claim 3

A system as defined in claim 2 wherein said computer provides compensation for deviation in said phase shift angle from -90* by dividing the difference between cross correlation functions by the sine of the angle of actual phase shift provided.

Claim 4

In a method for high-resolution spectral analysis of first and second signals from independent sources using a digital computer, wherein a desired convolution spectrum is translated to the origin without folding, the following steps: combining said first and second signals to provide a first product signal; shifting said second signal by approximately -90* to provide a phase-shifted second signal; combining said first signal and said phase-shifted second signal to provide a second product signal in quadrature with said first product signal; periodically sampling said first and second product signals to produce discrete signal samples; converting each of said discrete signal samples into a number in digital form, the value of said number being directly proportional to the amplitude of the sampled converted; and supplying to said digital computer each of said discrete signal samples in digital form for said spectral analysis.

Claim 5

A method as defined in claim 5, wherein said spectral analysis comprises: computing the sum of first and second autocorrelation functions R11( Tau ) and R22( Tau ); computing the difference of first and second cross-correlation functions R12( Tau ) and R21( Tau ); and computing by numerical integration said desired convolution spectrum in accordance with the following equation: where Tau is the sampling time.

Claim 6

A method as defined in claim 6, wherein said computer provides compensation for variations in gain in the production of said first and second product signals by normalizing said first and second autocorrelation functions, and said first and second cross-correlation functions.

Claim 7

A method as defined in claim 6, wherein said computer provides compensation for variation in phase shift of said phase shifted signal from -90* by computing said difference between cross-correlation functions from uncompensated difference between cross-correlation functions, and dividing said uncompensated difference by -sin phi , where phi is the value of actual phase shift in degrees.

Claim 8

The method defined in claim 5, wherein said spectral analysis comprises the following steps: computing two normalized correlation functions P11 and P22 and two normalized cross-correlation functions P12 and P21 from said first and second product signals, where the subscript digits 1 and 2 correspond to the first and second product signals, and the second digit of each subscript corresponds to a product signal delayed with respect to the other product signal; computing the sum P11 and P22 of said autocorrelation functions, and the difference of said normalized cross-correlation functions P21 - P12; and compensating for variations in phase shift of said phase shifted signal from -90* by dividing said difference P21 - P12 by -sin phi , where phi is the value of the actual phase shift in degrees; and finding the power spectral density G ( omega ) in accordance with the following equation: where Tau refers to the sampling time, the sum R11( Tau )+ R22( Tau ) is the sum of said autocorrelation functions, and the difference R21( Tau )- ( Tau ) is the phase shift compensated difference of said cross-correlation functions.

Claim 9

A method as defined In claim 9, wherein said computer provides compensation for variations in gain in the production of said first and second product signals by normalizing said autocorrelation and cross-correlation functions.