Characterizing the statistical properties of a biological signal

Claim 2

Method for characterizing the fluctuations of a signal representing an underlying biological process, said signal being intermittently obscured by a relatively independent process resulting in a corrupted signal comprising: noting the time intervals during which the obscuring process is occurring, constructing from the intervals a windowing function which makes a transition from one towards zero as the process obscures the signal and a transition towards one as the process terminates, and using the windowing function to weight the relative contributions of corresponding segments of the corrupted signal to create a new signal, whereby a characterization of the statistical properties of the new signal can be made to approximate the characterization of the statistical properties of the signal in the absence of the effect of the obscuring process.

Claim 3

The method of claim 1 wherein the weighting comprises computing the product of the windowing function and the corrupted signal to create the new signal, and wherein the fluctuations are characterized by an estimate of the autocorrelation function of the signal in the absence of the effect of the obscuring process comprising: computing the autocorrelation of the new signal, computing the autocorrelation of the windowing function, and computing the quotient of the autocorrelation function of the new signal and the autocorrelation of the windowing function.

Claim 4

The method of claim 2 further comprising computing a power spectrum estimate from the estimate of the autocorrelation function.

Claim 9

Method for characterizing the joint fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the first corrupted signal with the first windowing function to create a new first signal, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, and computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to produce an estimate of the crosscorrelation function between the two signals in the absence of the effects of the obscuring processes.

Claim 10

Method for characterizing the joint fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the first corrupted signal with the first windowing function to create a new first signal, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, and computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to produce an estimate of the crosscorrelation function between the two signals in the absence of the effects of the obscuring processes.

Claim 11

The method of claim 8 further comprising computing an estimate of the cross-spectrum of the first and second signals in the absence of the effects of the obscuring processes from the estimate of the crosscorrelation function.

Claim 12

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effect of the first obscuring process, computing an estimate of the power spectrum of the first signal in the absence of the effect of the first obscuring process from the estimate of the autocorrelation function, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to generate an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, computing from the estimate of the crosscorrelation function an estimate of the cross-spectrum of the two signals in the absence of the effects of the obscuring process, and computing the quotient of the estimates of the cross-spectrum and the power spectrum to generate an estimate of the transfer function between the two signals in the absence of the effects of the obscuring processes.

Claim 13

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effect of the first obscuring process, computing an estimate of the power spectrum of the first signal in the absence of the effect of the first obscuring process from the estimate of the autocorrelation function, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to generate an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, computing from the estimate of the crosscorrelation function an estimate of the cross-spectrum of the two signals in the absence of the effects of the obscuring process, and computing the quotient of the estimates of the cross-spectrum and the power spectrum to generate an estimate of the transfer function between the two signals in the absence of the effects of the obscuring processes.

Claim 14

The method of claim 10 further comprising computing the inverse Fourier transform of the estimate of the transfer function to generate an estimate of the impulse response function between the first and second signals in the absence of the effects of the obscuring processes.

Claim 15

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effects of the obscuring processes, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal and the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to produce an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, and directly computing an estimate of the impulse response function in the absence of the effects of the obscuring processes from the estimates of the crosscorrelation and the autocorrelation functions.

Claim 16

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effects of the obscuring processes, noting the time intervals during which the second obscuring process is occurring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal and the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to produce an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, and directly computing an estimate of the impulse response function in the absence of the effects of the obscuring processes from the estimates of the crosscorrelation and the autocorrelation functions.

Claim 17

The method of claim 12 further comprising computing the Fourier transform of the estimate of the impulse response function to generate an estimate of the transfer function between the first and second signals in the absence of the effects of the obscuring processes.

Claim 18

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effects of the obscuring processes, noting the time intervals during which the second obscuring process is occuring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to generate an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, computing an estimate of the cross-spectrum of the first and second signals in the absence of the effects of the obscuring processes from the estimate of the crosscorrelation function, and directly computing an estimate of the transfer function of the first and second signals in the absence of the effects of the obscuring processes from the estimates of the crosscorrelation function and the autocorrelation function.

Claim 19

Method for characterizing the fluctuations between a first signal representing a first underlying biological process, said first signal being intermittently obscured by a first process resulting in a first corrupted signal, and a second signal representing a second underlying biological process, said second signal being intermittently obscured by a second process (which may or may not be the same as the first obscuring process) resulting in a second corrupted signal in which each of the first and second signals are relatively independent of each of the first and second obscuring processes comprising: noting the time intervals during which the first obscuring process is occurring, constructing from the intervals a first windowing function which makes a transition from one towards zero as the first process obscures the first signal and a transition towards one as the first process terminates, computing the product of the first corrupted signal and the first windowing function to create a new first signal, computing the autocorrelation of the new first signal, computing the autocorrelation of the first windowing function, computing the quotient of the autocorrelation of the new first signal and the autocorrelation of the first windowing function to produce an estimate of the autocorrelation function of the first signal in the absence of the effects of the obscuring processes, noting the time intervals during which the second obscuring process is occuring, constructing from the second set of time intervals a second windowing function which makes a transition from one towards zero as the second process obscures the second signal and a transition towards one as the second process terminates, computing the product of the second corrupted signal with the second windowing function to create a new second signal, computing the crosscorrelation of the two new signals, computing the crosscorrelation of the two windowing functions, computing the quotient of the crosscorrelation of the new signals and the crosscorrelation of the windowing functions to generate an estimate of the crosscorrelation function of the two signals in the absence of the effects of the obscuring processes, computing an estimate of the cross-spectrum of the first and second signals in the absence of the effects of the obscuring processes from the estimate of the crosscorrelation function, and directly computing an estimate of the transfer function of the first and second signals in the absence of the effects of the obscuring processes from the estimates of the crosscorrelation function and the autocorrelation function.

Claim 22

The method of any of claim 8-14 wherein one of the signals is aterial blood pressure.

Claim 24

Method for characterizing the fluctuations of a signal representing an underlying biological process, said signal being intermittently obscured by a relatively independent process resulting in a corrupted signal comprising: noting the time intervals during which the obscuring process is occurring, constructing from the time intervals a windowing function which makes a transition from one towards zero as the process obscures the signal and a transition towards one as the process terminates, computing the product of the corrupted signal and the windowing function to create a new signal, computing the autocorrelation of the new signal, computing the autocorrelation of the windowing function, computing the quotient of the autocorrelation of the new signal and the autocorrelation of the windowing function, and computing an estimate of the power spectrum of the signal in the absence of the effect of the obscuring process from the quotient.

Claim 25

Method for characterizing the fluctuations of a signal representing an underlying biological process, said signal being intermittently obscured by a relatively independent process resulting in a corrupted signal comprising: noting the time intervals during which the obscuring process is occurring, constructing from the time intervals a windowing function which makes a transition from one towards zero as the process obscures the signal and a transition towards one as the process terminates, computing the product of the corrupted signal and the windowing function to create a new signal, computing the autocorrelation of the new signal, computing the autocorrelation of the windowing function, computing the quotient of the autocorrelation of the new signal and the autocorrelation of the windowing function, and computing an estimate of the power spectrum of the signal in the absence of the effect of the obscuring process from the quotient.