Deconvolution method for the analysis of data resulting from analytical separation processes

• US 5,748,491 A
• Filed: 12/20/1995
• Issued: 05/05/1998
• Est. Priority Date: 12/20/1995
• Status: Expired due to Term

• Current Assignee: Applied Biosystems LLC (Thermo Fisher Scientific Incorporated)
• Original Assignee: Perkinelmer Incorporated
• Inventors: Allison, Daniel B., Bowlby, James O. Jr.
• Primary Examiner(s): Voeltz, Emanuel T.
• Assistant Examiner(s): KEMPER, MELANIE A
• Application Number:
  US08/579,204
• Time in Patent Office: 867 Days
• Field of Search: 364/497, 364/553, 364/570, 364/572, 364/576, 364/724.04, 364/735
• US Class Current: 702/22
• CPC Class Codes: G01N 30/8617 Filtering, e.g. Fourier filtering
• CPC Class Codes: G06F 18/00 Pattern recognition
• CPC Class Codes: G06F 2218/02 Preprocessing

Abstract

An improved signal processing method in a signal processor for performing the deconvolution of a signal resulting from an analytical separation process is disclosed. In a first aspect, a signal representing a plurality of partially separated sample zones is measured, a point-spread-function of the signal is determined, and the Fourier transform of the signal and the point-spread-function is taken. Next, a noise component n of the signal is determined and the value of a result signal A(f) is calculated using the following filter ##EQU1## where D(f) is the Fourier transform of the signal, P(f) is the Fourier transform of the point-spread-function, and P*(f) is the complex conjugate of P(i). Finally, the inverse Fourier transform of the result A(f) is taken and reported as A(t). Preferably, the point-spread function is a Gaussian function having a standard deviation σ, where σ is determined using either an αβ tracker or the function σ=(a+bt²)^1/2, where a and b are constants. In a second aspect of the invention, a plurality of possible point-spread-functions of the signal are determined and the above-described method is applied using each PSF. The value of the largest point-spread-function which provides a nonnegative result is determined, and the associated value of A(t) is reported. In a third aspect of the invention, a program storage device readable by a machine, tangibly embodying a program of instructions executable by a machine to perform the method steps of the first or the second aspects of the invention is provided.

Claims

1. A signal processing method in a signal processor for identifying sample zones in a signal including multiple overlapping sample zones resulting from a separation process comprising the steps of:

receiving a signal generated by a detector which monitors the results of an analytical separation process, such signal representing a plurality of partially separated sample zones;

determining a point-spread-function of the signal;

converting the signal and the point-spread function from a time domain representation to a frequency domain representation using a Fourier transform;

determining a noise component of the signal;

calculating the value of a result signal A(f) using the formula ##EQU10## where D(f) is the Fourier transform of the signal, P(f) is the Fourier transform of the point-spread-function, P*(f) is the complex conjugate of P(f), and n is the noise component of the signal; and

converting the result signal A(f) from a frequency domain representation to a time domain representation by performing an inverse Fourier transform.

2. The method of claim 1 wherein the point-spread function is a Gaussian function having a standard deviation σ

.

3. The method of claim 2 wherein σ

is determined using an α

β

tracker including a constant term α and

a constant term β

.

4. The method of claim 3 wherein the value of α

is between 0.2 and 0.8.

5. The method of claim 3 wherein the value of a is between 0.4 and 0.6.

6. The method of claim 3 wherein β

=α

² /(2-α

).

7. The method of claim 2 wherein .σ

=(a+bt²)^1/2.

8. A signal processing method in a signal processor for identifying sample zones in a signal including multiple overlapping sample zones resulting from a separation process comprising the steps of:

receiving a signal generated by a detector which monitors the results of an analytical separation process, such signal representing a distribution of partially separated sample zones;

providing a plurality of possible point-spread-functions of the signal;

converting the signal and each of the point-spread functions from a time domain representation to a frequency domain representation by taking the Fourier transform of each;

providing an estimate of a noise component of the signal;

calculating a result signal A(f) for each point-spread-function, where ##EQU11## where D(f) is the Fourier transform of the signal, P(f) is the Fourier transform of the point-spread-function, P*(f) is the complex conjugate of P(f), and n is the noise component of the signal;

converting the result signal from the frequency domain to the time domain by taking the inverse Fourier transform of the result signal A(f) for each value of the point-spread function to give a result signal in the time domain A(t);

reporting the result signal A(t) in the time domain calculated using the largest value of the point-spread-function that provides a non-negative value of the result signal A(t).

9. A program storage device readable by a machine, tangibly embodying a program of instructions executable by a machine to perform method steps to identify sample zones resulting from a signal representing a plurality of partially separated sample zones, said method steps comprising:

receiving a signal generated by a detector which monitors the results of an analytical separation process, such signal representing a plurality of partially separated sample zones;

determining a point-spread-function of the signal;

converting the signal and the point-spread function from a time domain representation to a frequency domain representation by taking the Fourier transform of each;

determining a noise component of the signal;

calculating the value of a result signal A(f) using the formula ##EQU12## where D(f) is the Fourier transform of the signal, P(f) is the Fourier transform of the point-spread-function, P*(f) is the complex conjugate of P(f), and n is the noise component of the signal; and

converting the result signal A(f) from a frequency domain representation to a time domain representation by taking the inverse Fourier transform of the result signal.