Sample generation method and system for digital simulation processes
AssigneeThe DIRECTV Group, Inc.
InventorsErnest C. Chen, Paul R. Anderson, Joseph Santoru, Tammy G. Liu
Life of this patent
Estimating the term…
Abstract
A method for generating a set of random numbers with statistics represented by a cumulative density function (CDF) includes generating a set of uniformly spaced samples between an upper limit and a lower limit. Each of the uniformly spaced samples are then mapped to a corresponding value on a cumulative density function curve. The set of uniformly spaced samples are then scrambled to randomize the samples. Companding may also be incorporated in the sample generation process.
Claims26
A method for generating and analyzing random sample values on a computer, said method comprising the steps of:
- (a) generating a set of numbers that are substantially uniformly distributed between an upper numerical limit and a lower numerical limit;
- (b) utilizing a computer to map each one of said numbers to a corresponding sample value on a cumulative density function (CDF) curve;
- (c) collecting each said sample value into an ordered set of sample values;
- (d) scrambling said ordered set of sample values so as to reorder said sample values in a substantially random manner and thereby form a random set of sample values;
- (e) utilizing said random set of sample values to form a histogram-type output;
- and
- (f) presenting the output on a display for statistical analysis.
A method for generating and analyzing random sample values on a computer according to a probability density function (PDF), said method comprising the steps of:
- (a) generating a set of numbers that are substantially uniformly distributed and spaced apart between an upper numerical limit and a lower numerical limit;
- (b) utilizing a computer to map each one of said numbers to a corresponding sample value on a cumulative density function (CDF) curve, which is mathematically related to said probability density function and represented by a look-up table stored on said computer;
- (c) collecting each said sample value into an ordered set of sample values;
- (d) scrambling said ordered set of sample values so as to reorder said sample values in a substantially random manner and thereby form a random set of sample values;
- (e) utilizing said random set of sample values to form histogram-type output;
- and
- (f) presenting the output on a display for statistical analysis.
The method of 17, wherein said companding is at least partially accomplished by:
- reducing the spacing between said numbers in at least one section between said upper numerical limit and said lower numerical limit so as to ensure that a sufficient amount of corresponding sample values can be successfully collected from any low-probability area defined by said cumulative density function curve and that any said low-probability area is therefore not disproportionately underrepresented by said sample values;
- and
- increasing the spacing between said numbers in at least one other section between said upper numerical limit and said lower numerical limit so as to ensure that a sufficient amount of corresponding sample values can be successfully collected from any high-probability area defined by said cumulative density function curve while also ensuring that said high-probability area is not disproportionately overrepresented by said sample values.
A system for generating and analyzing random sample values on a computer, said system comprising:
- a computer;
- and
- a look-up table stored on said computer;
- wherein said computer is operable to
- (a) generate a set of numbers that are substantially uniformly distributed between an upper numerical limit and a lower numerical limit;
- (b) map each one of said numbers to a corresponding sample value on a cumulative density function (CDF) curve that is represented by said look-up table;
- (c) collect each said sample value into an ordered set of sample values;
- (d) scramble said ordered set of sample values so as to reorder said sample values in a substantially random manner and thereby form a random set of sample values;
- (e) utilize said random set of sample values for form a histogram-type output;
- and
- (f) present the output on a display for statistical analysis.
Dependencies are inferred from the claim text.