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Methods and apparatus for computing the input and output signals of a linear shift-variant system

  • US 20060101106A1
  • Filed: 09/26/2005
  • Published: 05/11/2006
  • Est. Priority Date: 11/08/2004
  • Status: Active Grant
First Claim
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1. A method of computing the output signal g(x)of a Linear Shift-Variant System (LSVS) where x is an m-dimensional variable, said output corresponding to an input signal f(x), said LSVS characterized by a Shift-Variant Point Spread Function (SV-PSF) h(x,α

  • ), said method comprising a. Computing a set of Rao Transform (RT) coefficients Sn of said input signal f(x) with respect to said SV-PSF h(x,α

    ) wherein said Rao Transform (RT) is defined by an expression that is a definite integral with respect to α

    of the product of h(x−

    α



    ) and f(x−

    α

    ), said coefficients Sn obtained by;

    1. substituting a truncated Taylor series expansion of h(x−

    α



    ) around the point (x,α

    ) in said expression that defines RT, 2. substituting a truncated Taylor series expansion of f(x−

    α

    ) around the point x in said expression that defines RT, 3. simplifying said expression after the substitutions above as a sum of a set of product terms wherein each product term is the result of multiplying a derivative of f(x) with respect to x at x and a coefficient that determines Sn and expressed in terms of a set of moments with respect to a of the zero-th and higher order derivatives with respect to x of said SV-PSF h;

    b. computing a set of derivatives f(n) of f(x) with respect to x at x of said input signal f(x);

    c. computing a set of product terms obtained by multiplying each RT coefficient Sn by its corresponding input signal derivative f(n), d. summing or adding all members of said set of product terms to obtain the output signal g(x) of said LSVS.

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