# US 2013/0158922 A1 · Estimation of a quantity related to impedance > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2013/0158922 A1 - Document ID: US20130158922A1 - Status: Published application - Kind: A1 - Application number: 13/331,200 - Filed: 2011-12-20 - Published: 2013-06-20 - Earliest claimed: 2011-12-20 - Assignees: Telefonaktiebolaget L M Ericsson (publ) - Inventors: Antoni Fertner; Henrik Almeida; Miguel Berg; Per Ola Börjesson; Klas Ericson; Fredrik Lindqvist - Web page: https://patentgrep.com/patent/US20130158922A1 ## CPC - H04B 3/46: Monitoring; Testing - H04B: TRANSMISSION ## Abstract Method, arrangement and network node/device for estimating a quantity related to impedance in a first frequency interval, D1, of a telecommunication transmission line where the transmission line has a length d. The method involves determining a quantity related to impedance of the telecommunication transmission line for at least two frequencies, f1D2 and f2D2, in a second frequency interval D2. The frequencies f1D2 and f2D2 should fulfil the condition that the line length d times the absolute value of the difference between a line propagation constant γ(f1)D2 and a line propagation constant, γ(f2)D2, is less than π, i.e. abs(d*γ(f1)D2−d*γ(f2)D2)<π. The method further involves estimating a quantity related to impedance in the first frequency interval D1 based on the determined quantity related to impedance in the second frequency interval D2, where the estimating involves the fitting of a Puiseux series to the determined quantity related to impedance in frequency interval D2. ## Claims ### Claim 1 Method for estimating a quantity related to impedance in a first frequency interval, D1, of a telecommunication transmission line having a length d, the method comprising: determining a quantity related to impedance of the telecommunication transmission line for at least two frequencies, f1D2 and f2D2, in a second frequency interval D2, for which frequencies the line length d times the absolute value of the difference between a line propagation constant γ(f1)D2 and a line propagation constant, γ(f2)D2, is less than π, i.e. abs(d*γ(f1)D2−d*γ(f2)D2)<π; and estimating a quantity related to impedance in the first frequency interval D1 based on the determined quantity related to impedance in the second frequency interval D2; wherein the estimating involves the fitting of a Puiseux series to the determined quantity related to impedance in frequency interval D2. ### Claim 2 (depends on 1) Method according to claim 1, wherein the Puiseux series contain integer and/or half integer powers of frequency. ### Claim 3 (depends on 1) Method according to claim 1, wherein the Puiseux series is represented by a Laurent or Taylor series with only even powers of the angular frequency in the real part and only odd powers of the angular frequency in the imaginary part. ### Claim 4 (depends on 1) Method according to claim 1, wherein the quantity related to impedance is estimated for a frequency f1D1 in frequency interval D1 and where the relation between the concerned frequencies in the frequency intervals D1 and D2 is such that: max(abs(d*γ(f1)D2−d*γ(f1)D1),abs(d*γ(f2)D2−d*γ(f1)D1))<π ### Claim 5 (depends on 1) Method according to claim 1, wherein at least one frequency in D1 is lower than the lowest frequency in D2. ### Claim 6 (depends on 1) Method according to claim 1, wherein the estimating further involves: determining a function which is valid in D1, by use of coefficients from the Puiseux series fitted to the quantity determined in frequency interval D2. ### Claim 7 (depends on 6) Method according to claim 6, wherein said function is one of: a rational function; a Puiseux series different from the Puiseux series fitted to the quantity determined in frequency interval D2. ### Claim 8 (depends on 1) Method according to claim 1, wherein the transmission line has a first and a second end, and the determining is based on at least one of: an echo measurement performed in the first end of the transmission line; an impedance measurement performed in the first end of the transmission line. ### Claim 9 (depends on 1) Method according to claim 1, further comprising: applying a smoothing function, in the frequency plane, to a transition region between determined and estimated values. ### Claim 10 (depends on 9) Method according to claim 9, wherein the transition region is a frequency region where the first frequency interval D1 and the second frequency interval D2 overlap. ### Claim 11 (depends on 10) Method according to claim 10 wherein the smoothing function is a linear combination of determined and estimated values, where the estimated values are given a higher weight in one end of the transition region, and lower weight in the other end of the transition region. ### Claim 12 (depends on 1) Method according to claim 1, wherein a SELT postprocessing (SELT-P) is performed on the transmission line, which SELT-P involves a transformation of a quantity related to the estimated quantity related to impedance in the first frequency interval D1 between a frequency plane and a time plane, which transformation involves the applying of a windowing function centered approximately around f=0. ### Claim 13 (depends on 1) Method according to claim 1, wherein a SELT postprocessing (SELT-P) is performed on the transmission line, which SELT-P involves a transformation of a quantity related to the estimated quantity related to impedance in the first frequency interval D1 between a frequency plane and a time plane, which transformation involves the applying of a windowing function starting approximately at f=0. ### Claim 14 Arrangement for estimating a quantity related to impedance in a first frequency interval, D1, of a telecommunication transmission line having a length d, said arrangement comprising processing circuitry configured to: determine a quantity related to impedance of the telecommunication transmission line for at least two frequencies, f1D2 and f2D2, in a second frequency interval D2, for which frequencies the line length d times the absolute value of the difference between a line propagation constant γ(f1)D2 and a line propagation constant, γ(f2)D2, is less than π, i.e. abs(d*γ(f1)D2−d*γ(f2)D2)<π; and estimate a quantity related to impedance in the first frequency interval D1 based on the determined quantity related to impedance in the second frequency interval D2, wherein the estimating involves the fitting of a Puiseux series to the determined quantity related to impedance in frequency interval D2. ### Claim 15 (depends on 14) Arrangement according to claim 14, wherein the Puiseux series contain integer and/or half integer powers of frequency. ### Claim 16 (depends on 14) Arrangement according to claim 14, wherein the Puiseux series is represented by a Laurent or Taylor series with only even powers of the angular frequency in the real part and only odd powers of the angular frequency in the imaginary part. ### Claim 17 (depends on 14) Arrangement according to claim 14, wherein the quantity related to impedance is estimated for a frequency f1D1 in frequency interval D1 and where the relation between the concerned frequencies in the frequency intervals D1 and D2 is such that: max(abs(d*γ(f1)D2−d*γ(f1)D1),abs(d*γ(f2)D2−−d*γ(f1)D1))<π ### Claim 18 (depends on 14) Arrangement according to claim 14, wherein at least one frequency in D1 is lower than the lowest frequency in D2. ### Claim 19 (depends on 14) Arrangement according to claim 14, wherein the estimating further involves: determining a function which is valid in D1, by use of coefficients from the Puiseux series fitted to the quantity determined in frequency interval D2. ### Claim 20 (depends on 19) Method according to claim 19, wherein said function is one of: a rational function; a Puiseux series different from the Puiseux series fitted to the quantity determined in frequency interval D2. ### Claim 21 (depends on 14) Arrangement according to claim 14, wherein the transmission line has a first and a second end, and the processing circuitry is further configured to determine the quantity based on one of: an echo measurement performed in the first end of the transmission line; an impedance measurement performed in the first end of the transmission line. ### Claim 22 (depends on 14) Arrangement according to claim 14, wherein the processing circuitry is further configured to apply a smoothing function, in the frequency plane, to a transition region between determined and estimated values. ### Claim 23 (depends on 22) Arrangement according to claim 22, wherein the transition region is a frequency region where the first frequency interval D1 and the second frequency interval D2 overlap. ### Claim 24 (depends on 23) Arrangement according to claim 23, wherein the smoothing function is a linear combination of determined and estimated values, where the estimated values are given a higher weight in one end of the transition region, and lower weight in the other end of the transition region. ### Claim 25 (depends on 14) Arrangement according to claim 14, wherein the processing circuitry is further configured to perform SELT postprocessing (SELT-P) on the transmission line, which SELT-P involves a transformation of a quantity related to the estimated quantity related to impedance in the first frequency interval D1 between a frequency plane and a time plane, which transformation involves the applying of a windowing function centered approximately around f=0. ### Claim 26 (depends on 14) Arrangement according to claim 14, wherein the processing circuitry is further configured to perform SELT postprocessing (SELT-P) on the transmission line, which SELT-P involves a transformation of a quantity related to the estimated quantity related to impedance in the first frequency interval D1 between a frequency plane and a time plane, which transformation involves the applying of a windowing function starting approximately at f=0. ### Claim 27 (depends on 14) Device comprising an arrangement according to claim 14. ### Claim 28 (depends on 14) Network node comprising an arrangement according to claim 14. ### Claim 29 (depends on 1, 14) Computer program, comprising computer readable code means, which when run in an arrangement or device according to claim 14 causes the device to perform the corresponding method according to claim 1. ### Claim 30 (depends on 29) Computer program product, comprising the computer program according to claim 29.