Method of and arrangement for restoring invalid samples of an equidistantly sampled signal

Claim 3

A method as claimed in claim 1, in which the sampling rate of said received signal is f s and said number N of stored consecutive samples s k is N=2 fs/f.sub.min +m, wherein f min is a frequency corresponding to said maximum anticipated periodicity of said signal segment.

Claim 4

A method as claimed in claim 1, further comprising: determining whether the number m of invalid samples exceeds or is less than the quantity q+1; if m≦q, setting the vector x equal to the vector z; if m≧q+1, converting the matrix G into a product LU by means of LU-decomposition, wherein L and U respectively represent a lower triangular matrix and an upper triangular matrix of (m×m) elements, the elements L kk and U kk thereof which differ from zero being given by ##EQU24## solving the system of equations Ly=z to derive y; and solving the system of equations x=y, to derive x.

Claim 5

Apparatus for providing correct samples to replace invalid samples of an equidistantly sampled received signal, each invalid sample being identified by a flag bit in said received signal, correct samples being derived from a segment of said received signal which includes said invalid samples, such apparatus comprising: detection means responsive to a sequence of consecutive flag bits in said received signal to produce a flag signal identifying the corresponding sequence of consecutive invalid samples in said received signal; control means and a memory coupled to said detection means, said control means being responsive to said flag signal to store in said memory a sequence of N consecutive samples s k of a segment of said received signal which includes as a subsequence therein said sequence of consecutive invalid samples s t (i) to be replaced, wherein k=0, 1, . . . , N-1, and i=1, . . . , m, said number N including a number of valid samples of said received signal corresponding to a predetermined maximum anticipated periodicity of such signal during said segment thereof; and computing means coupled to said memory and programmed so as to (a) determine from said stored sequence of samples s k a quantity q representing a number of such samples corresponding to the periodicity of said received signal during said segment thereof; (b) determine a vector z for said subsequence of invalid samples s t (i), such determination being made by adding together pairwise, after scaling by a constant scaling coefficient "a", a number qn of said stored samples s k located before and an equal number qn of said stored samples s k located after each of said invalid samples s t (i), n being an integer such that qn corresponds to said maximum anticipated periodicity; (c) form a system of autoregression equations with a number of unknown quantities equal to said number of m of invalid samples s t (i), such equations being of the form Gx=z, wherein G is an (m×m) matrix and x is an m-vector containing elements x i , an element x i being an estimated corrected value of an invalid signal samples s t (i) ; (d) solve said system of equations Gx=z to derive the m values of x i ; and (e) provide m output signal samples having said corrected values x i as replacements for the m invalid signal samples s t (i).

Claim 6

Apparatus for providing correct samples to replace invalid samples of an equidistantly sampled received signal, each invalid sample being identified by a flag bit in said received signal, correct samples being derived from a segment of said received signal which includes said invalid samples, such apparatus comprising: detection means responsive to a sequence of consecutive flag bits in said received signal to produce a flag signal identifying the corresponding sequence of consecutive invalid samples in said received signal; control means and a memory coupled to said detection means, said control means being responsive to said flag signal to store in said memory a sequence of N consecutive samples s k of a segment of said received signal which includes as a subsequence therein said sequence of consecutive invalid samples s t (i) to be replaced, wherein k=0, 1, . . . , N-1, and i=1, . . . , m, said number N including a number of valid samples of said received signal corresponding to a predetermined maximum anticipated periodicity of such signal during said segment thereof; and computing means coupled to said memory and programmed so as to (a) determine from said stored sequence of samples s k a quantity q representing a number of such samples corresponding to the periodicity of said received signal during said segment thereof; (b) determine a vector z for said subsequence of invalid samples s t (i), such determination being made by adding together pairwise, after scaling by a constant scaling coefficient "a", a number qn of said stored samples s k located before and an equal number qn of said stored samples s k located after each of said invalid samples s t (i), n being an integer such that qn corresponds to said maximum anticipated periodicity; (c) form a system of autoregression equations with a number of unknown quantities equal to said number of m of invalid samples s t (i), such equations being of the form Gx=z, wherein G is an (m×m) matrix and x is an m-vector containing elements x i , an element x i being an estimated corrected value of an invalid signal samples s t (i) ; (d) solve said system of equations Gx=z to derive the m values of x i ; and (e) provide m output signal samples having said corrected values x i as replacements for the m invalid signal samples s t (i).

Claim 7

Apparatus as claimed in claim 4, further comprising comparator means for comparing the values of m and q and supplying a command signal to said computing means when m≧q+1, and said computing means is further programmed so that in response to said command signal it: (f) converts said matrix G into a product LU by means of LU-decomposition, wherein L and U respectively represent a lower triangular matrix and an upper triangular matrix of (m×m) elements, the elements L kk and U kk thereof which differ from zero being given by ##EQU25## c being a predetermined constant periodicity coefficient; and (g) solves a system of equations L y=z to derive y, and solves a system of equation Ux=y to derive x.

Claim 8

Apparatus as claimed in claim 5, wherein said computing means further comprises a further memory for storing a table of predetermined values of the elements of said L-matrix and said U-matrix of said product LU.