System and method of data reduction for improved exponential decay measurements
First Claim
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1. A method for determining an exponential decay rate of a signal in the presence of noise, said method comprising:
- receiving an exponentially decaying signal from a detector;
digitizing said signal to form a first array of data points;
estimating a baseline value of said signal by averaging a final fraction of said data points;
subtracting said baseline value from said first array to generate a second array;
identifying a last data point on said second array occurring before a negative or nil valued data point on said second array;
scaling an ordinate value of said last data point by a factor greater than unity to determine a new first data point for a baseline fit on said first array;
fitting remaining data on said first array to a straight line to determine an estimate for a sloping baseline and said noise;
subtracting said straight line from said data points to establish a resulting array;
identifying a last data point on said resulting array occurring before a negative or nil valued data point on said resulting array;
performing a logarithmic transformation of said resulting array up to said last data point on said resulting array; and
determining said decay rate of said signal.
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Abstract
A novel system and method for data reduction for improved exponential decay rate measurement in the present of excess low frequency noise. The system and method fit the tail of a record to a straight line wherein the straight line is extrapolated to the entire record and then subtracted from the initial data points before a logarithmic transformation is taken.
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Citations
24 Claims
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1. A method for determining an exponential decay rate of a signal in the presence of noise, said method comprising:
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receiving an exponentially decaying signal from a detector;
digitizing said signal to form a first array of data points;
estimating a baseline value of said signal by averaging a final fraction of said data points;
subtracting said baseline value from said first array to generate a second array;
identifying a last data point on said second array occurring before a negative or nil valued data point on said second array;
scaling an ordinate value of said last data point by a factor greater than unity to determine a new first data point for a baseline fit on said first array;
fitting remaining data on said first array to a straight line to determine an estimate for a sloping baseline and said noise;
subtracting said straight line from said data points to establish a resulting array;
identifying a last data point on said resulting array occurring before a negative or nil valued data point on said resulting array;
performing a logarithmic transformation of said resulting array up to said last data point on said resulting array; and
determining said decay rate of said signal. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A ring-down cavity system for determining an exponential decay rate of a signal in the presence of noise comprising:
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a ring-down cavity;
a light source for injecting light into said cavity;
a dectector;
a digitizer; and
a processor for determing said decay rate by fitting a straight line to a curve associated with said decay rate at a time greater than where a negative or nil value is detected, removing undesirable data associated with said noise and logarithmically transforming said data. - View Dependent Claims (17, 18, 19, 20, 21)
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22. A method for processing a data record to determine an associated decay rate of a species in the presence of noise, said method comprises:
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subtracting a DC offset from said data record;
determining a time associated with a first data point occuring before a first negative or nil data point of said data record;
scaling said time by a factor greater than unity to determine an end time associated with a portion of said data record, said end time having a corresponding value;
averaging data points from said time value to the end of record;
subtracting said value from each data point from said data record to create a new data record;
determining an end point for said new data record associated with a first data point before a first negative or nil data point of said new data record;
logarithmically transforming said new data record; and
determining a decay rate from said logarithmic transform.
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23. A method of measuring the decay rate of a signal having noise, said method comprising:
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measuring a data signal having noise;
forming a data array having data values associated with said signal;
subtracting undesirable data values from said array;
establishing a resulting array;
testing said resulting array for a first negative or nil value;
forming a new array ending at one value before said first negative or nil value;
performing a logarithmic transformation on said new array; and
determining said decay rate from said logarithmic transformation.
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24. A method for determining an exponential decay rate of a signal in the presence of noise, said method comprising:
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receiving an exponentially decaying signal;
digitizing said signal;
removing an estimated noise value from said signal;
identifying a cutoff point associated with said signal;
scaling said cutoff point by a factor greater than unity;
determining a new estimated noise value;
removing said new estimated noise value from said signal;
identifying a last point of said signal before a negative or nil valued data point on said resulting array; and
performing a logarithmic transformation to determine said decay rate of said signal.
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Specification