EP0146988A1
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EP
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Method of correcting erroneous values of samples of an equidistantly sampled signal and device for carrying out the method
Assignee: Koninklijke Philips NV
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Filing: 1984-12-03
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Granted: —
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Expires: 2004-12-03
Abstract
Abstract The values of incorrect samples of, for example, a digital audio signal are estimated by means of interpolation. For this purpose an appropriate sampling interval is determined from the number of incorrect samples, in which interval the incorrect samples are situated. Subsequently, a best-fitting recursion formula is determined from the values of the samples, a first estimate being taken for the values of the incorrect samples. By means of this recursion formula the value of a sample is expressed as a weighted sum of the values of a number of preceding samples and an error term. By means of the recursion formula thus found the values of the incorrect samples are subsequently estimated, in such a manner that they are best-fitting values for the recursion formula. The Application also discloses a device for carrying out the method.
Inventors
- 👤 Augustus Josephus E.M. Janssen
- 👤 Raymond Nicolaas Johan Veldhuis
- 👤 Hendrik Johan Prins
- 👤 Lodewijk Barend Vries
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-11-01 07:43
CPC Classifications
H; H03; H03M; H03M7/00; G; G11; G11B; G11B20/00; G11B20/10; G11B20/18; G11B20/1806; G11B20/1876
Claims Analysis
Total Claims: 32
Claim 1
Independent Claim
108 words
A method of correcting erroneous values of samples of an equidistantly sampled signal by interpolation, characterized in that from the number of incorrect samples a corresponding sampling interval is derived within which the incorrect samples are situated, a best-fitting recursion formula is determined from the values of the samples in said sampling interval, a first estimate being taken for the values of the incorrect samples, by means of which recursion formula the value of a sample is expressed as a weighted sum of the values of a number of preceding samples and an error term, and the values of the incorrect samples are estimated with said recursion formula.
Claim 2
Independent Claim
108 words
A method of correcting erroneous values of samples of an equidistantly sampled signal by interpolation, characterized in that from the number of incorrect samples a corresponding sampling interval is derived within which the incorrect samples are situated, a best-fitting recursion formula is determined from the values of the samples in said sampling interval, a first estimate being taken for the values of the incorrect samples, by means of which recursion formula the value of a sample is expressed as a weighted sum of the values of a number of preceding samples and an error term, and the values of the incorrect samples are estimated with said recursion formula.
Claim 3
Dependent Claim
164 words
.1 A method as claimed in Claim 1, characterized in that for determining the weighting factors of the weighted sum of the recursion formula the following steps are carried out: - drawing up a recursions formula for a number of samples within the interval, which formula contains a weighted sum of the.values of a number of preceding samples, the difference between the value of a sample and the value of the weighted sum being expressed as an error term, a first estimate being taken for the values of the incorrect samples and the number of samples for which a recursion formula is drawn up being substantially equal to the difference between the number of samples in the interval and the number of samples whose values are weighted in the weighted sum, - determining the error energy corresponding to the error terms and averaged over the samples in the interval, and - minimizing the error energy as a function of each of the weighting factors.
Claim 4
Dependent Claim
50 words
A method as claimed in Claim 1 or 2, characterized in that for determining the weighting factors of the weighted sum of the recursion formula the system of equations to be solved of the form: see formula (20), is replaced by a Toeplitz system of the form: see formula (21).
Claim 5
Dependent Claim
22 words
A method as claimed in Claim 3, characterized in that the estimators for the autocorrelation coefficients are given by: see formula (7).
Claim 6
Dependent Claim
42 words
A method as claimed in Claim 3 or 4, characterized in that for computing the estimators for the autocorrelation coefficients the values of the samples are described with a lower degree of quantization than the actual degree of quantization of the samples.
Claim 7
Dependent Claim
44 words
A method as claimed in Claim 4 or 5, characterized in that for calculating the estimators of the autocorrelations coefficients the result of a multiplication of the values of two samples is looked up in a table containing the possible results of the multiplication.
Claim 8
Dependent Claim
27 words
A method as claimed in Claim 3, 4, 5 or 6, characterized in that the Toeplitz system R,a=b 2 is solved by means of the Levinson-Durbin algorithm.
Claim 9
Dependent Claim
26 words
A method as claimed in Claim 1, characterized in that a predetermined value is adopted for the maximum number p of samples in the recursion formula.
Claim 10
Dependent Claim
26 words
A method as claimed in Claim 1, characterized in that maximum number p of samples of the recursion depends on the number m of incorrect samples.
Claim 11
Dependent Claim
27 words
A method as claimed in Claim 9, characterized in that the maximum number p of samples increases as a linear function of the number of incorrect samples.
Claim 12
Dependent Claim
52 words
A method as claimed in Claim 10, characterized in that the signal is an audio signal which is sampled with a frequency of substantially 44.1 kHz and the relationship between the maximum number p of samples of the recursion and the number m of incorrect samples is given by p ≈ 3m+2.
Claim 13
Dependent Claim
27 words
A method as claimed in Claim 1, characterized in that the number N of samples in the interval is determined by the number m of incorrect samples.
Claim 14
Independent Claim
26 words
A method as claimed in Claim'12, characterized in that the number N of samples increases as a linear function of the number m of incorrect samples.
Claim 15
Dependent Claim
50 words
A method as claimed in Claim 10, characterized in that the signal is an audio signal which is sampled with a frequency of substantially 44.1 kHz and the relationship between the number N of samples in the interval and the number of incorrect samples is given by N ≈ 32m.
Claim 16
Dependent Claim
182 words
15 . A method as claimed in any one of the preceding Claims, characterized in that for estimating the values of the incorrect samples the following steps are carried out: - within the first interval in which the incorrect samples are situated a second interval is determined whose first sample is situated at least a number of samples equal to the number of samples in the recursion formula before the first incorrect sample and whose last sample is situated at least a number of samples equal to the number of samples in the recursion formula after the last incorrect sample, - for at least the samples from-the first incorrect sample up to and including the last sample in the second interval the recursion formula is drawn up with the computed weighting factors, - the error energy which averaged over the relevant samples in the interval and corresponding to the error terms of the recursion formulas is determined, and - the estimates of the incorrect samples are determined by minimizing the error energy as a function of the values of the incorrect samples.
Claim 17
Dependent Claim
39 words
A method as claimed in Claim 15, characterized in that the recursion formulae constitute the system of recursion equations of the form: see formula (10), and this system is converted into a system of the form: see formula (12).
Claim 18
Dependent Claim
60 words
A method as claimed in Claim 16, characterized in that by means of the system Ax+By=e the equation for the error energy averaged over the relevant samples in the interval is converted into an equation of the form: see formula (13), in which the vector x min for which the error energy is minimal is given by: see formula (14).
Claim 19
Dependent Claim
22 words
A method as claimed in Claim 17, characterized in that the vector x. is computed by solving the system: see formula (15).
Claim 20
Dependent Claim
37 words
A method as claimed in Claim 18, characterized in that the incorrect samples are situated at consecutive instants t 1 , ... tm and the system Vxmin . =w is solved by means of the Levinson algorithm.
Claim 21
Independent Claim
56 words
A method as claimed in any one of the preceding Claims, characterized in that the method is repeated at least one time, the weighting factors of the best-fitting recursion formula being computed from the values of the correct samples in the interval and the values of the incorrect samples as estimated by means of the method.
Claim 22
Dependent Claim
75 words
A device for carrying out the method as claimed in Claim 1, characterized in that the device comprises: - input means for entering the values of samples of the sampled signal, - detection means for detecting incorrect samples, - first computing means for estimating the best-fitting recursion formula, - second computing means for estimating the values of the incorrect samples, and - output means for feeding out the values of samples of the sampled signal
Claim 23
Dependent Claim
44 words
A device as claimed in Claim 21, characterized in that the first computing means comprise: - means for computing the number of samples in the interval, and - means for computing the maximum number of samples in the weighted sum of the recursion formula.
Claim 24
Dependent Claim
30 words
A device as claimed in Claim 22, characterized in that the first computing means further comprise means for computing the weighting factors of the weighted sum of the recursion formula.
Claim 25
Dependent Claim
40 words
A device as claimed in Claim 23, characterized in that the means for computing the weighting factors are provided with: - means for computing the autocorrelation coefficients: see formula (7), and - means for solving the system: see formula (16).
Claim 26
Dependent Claim
31 words
A device as claimed in Claim 24, characterized in that the means for computing the autocorrelation coefficients comprise means for reducing the degree of quantization of the values of the samples.
Claim 27
Dependent Claim
42 words
A device as claimed in Claim 23 or 24, characterized in that the means for computing the autocorrelation coefficients comprise means for determining the product of the values of two samples by means of a table of possible values of this product.
Claim 28
Dependent Claim
24 words
A device as claimed in Claim 24, 25 or 26, characterized in that the means for solving the system Ra=b comprise the Levinson-Durbin algorithm.
Claim 29
Independent Claim
40 words
A device as claimed in any one of the Claims 21 to 27, characterized in that the second computing means comprise: - means for computing the numbers: see formula (17), and - means for computing the numbers: see formula (18).
Claim 30
Dependent Claim
24 words
A device as claimed in Claim 28, characterized in that the second computing means further comprise means for solving the system: see formula (19).
Claim 31
Dependent Claim
33 words
A device as claimed in Claim 29, where S t1 , ... S tm are consecutive samples, characterized in that the means for solving the system Vxmin . =w comprise a Levinson algorithm.
Claim 32
Independent Claim
55 words
An apparatus for reproducing digital information from a carrier, in particular an optically readable record carrier on which digital information is stored in the form of optically detectable areas alternating with intermediate areas, characterized in that the apparatus is provided with a device as claimed in any one of the preceding Claims 21 to 30.
References Cited (Backward Citations)
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