WO2001053981A1 - A method and a device for signal processing - Google Patents
A method and a device for signal processing Download PDFInfo
- Publication number
- WO2001053981A1 WO2001053981A1 PCT/SE2000/002627 SE0002627W WO0153981A1 WO 2001053981 A1 WO2001053981 A1 WO 2001053981A1 SE 0002627 W SE0002627 W SE 0002627W WO 0153981 A1 WO0153981 A1 WO 0153981A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- signal
- fourier transformation
- word length
- discrete fourier
- signals
- Prior art date
Links
- 238000000034 method Methods 0.000 title claims abstract description 25
- 230000009466 transformation Effects 0.000 claims abstract description 88
- 238000012937 correction Methods 0.000 claims abstract description 32
- 238000000844 transformation Methods 0.000 claims abstract description 18
- 238000004458 analytical method Methods 0.000 claims description 9
- 230000015572 biosynthetic process Effects 0.000 claims description 4
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 230000002311 subsequent effect Effects 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 2
- 238000004364 calculation method Methods 0.000 description 3
- 230000001419 dependent effect Effects 0.000 description 3
- 238000001914 filtration Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 229920000136 polysorbate Polymers 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
Definitions
- the present invention relates to a method for signal processing, in which a Discrete Fourier Transformation (DFT) having a restricted word length is applied on a signal in digital state and a device for such signal processing.
- DFT Discrete Fourier Transformation
- the signals may be of any type and being deliberately transmitted by a transmitter or resulting from any physical phenomena of an arbitrary object, such as vibrations caused by electromagnetical or other influences by any object.
- a component moveable in for example an industrial process may be mentioned, said component transmitting a sig- nal having a frequency varying to a component being stationary in the space and receiving the signal reflected by the stationary object through a receiver for finding its position in the space by means of a frequency analysis in the form of a Discrete Fourier Transformation of a signal obtained by forming a difference be- tween the transmitted and received signal with respect to the frequency composition thereof.
- Transformation having a restricted word length often results in the introduction of systematical errors and a degraded dynamic of the result of the transformation results in the form of a higher noise level with respect to the level of the signal on which the signal processing is applied, which in certain cases means that the information desired to be obtained from the signal may not at all be extracted therefrom but will completely drown in the noise.
- a reason for the choice to carry out a said Discrete Fourier Transformation having a restricted word length in spite of that is that it is mostly in the practise not possible to make the analysis at a full word length, since this would take far too long time.
- truncating errors are by that generated, i.e. errors being a consequence of the use of too few bit at the Discrete Fourier Transformation , for example 8-12 bit instead of 16 , having the problems mentioned above as a consequence.
- the object of the present invention is to provide a method and a device making it possible to solving the problems mentioned above of such methods and devices already known to a large extent.
- This object is according to the invention obtained by providing a method of the type defined in the introduction, in which a) a plurality of samples are taken from a signal in digital state and said Discrete Fourier Transformations are applied on these samples, b) a mean value of the results of these transformations is calculated , c) the calculated mean value is compared with a known ideal value for a result of a said transformation of said signal without any systematical errors emanating from a restricted word length, and after that in connection with subsequent Dis- crete Fourier Transformations having a restricted word length of signals a correction is made depending upon the deviation between said mean value and the ideal value established by said comparison.
- this signal which is used for determining how the error correction of subsequent signals is to take place, should be linear.
- the signal used for arriving to the deviation in question for a later correction has to be the same signal as the signal intended to be processed and analysed through said Discrete Fourier Transformation having a restricted word length later on.
- a long sequence of a random noise signal of the type of coloured noise having a representative distribution or white Gauss noise could for example instead be selected as such a signal. Neither is it necessary that the expected ideal value for a said transformation, i.e.
- the value which had been obtained if a full word length had been used is zero, so that for example a part of the value obtained at the mean value formation will be later on subtracted in connection with the Discrete Fourier Transformation of a signal, but would this ideal result be zero, would exactly the result obtained by the mean value formation be subtracted.
- the systematical error resulting from a given Discrete Fourier Transformation having a restricted word length is determined by carrying out the steps a)-c) one single time, and after that said correction is carried out at subsequent Discrete Fourier Transformations having a restricted word length of signals without any repetition of the steps a)-c).
- This way to proceed is very advantageous, since the same systematical errors result and the same error correction is asked for all the time when using the same Discrete Fourier Transformation, so that there would mostly make no sense to repeat the error correction calculation.
- the steps a)-c) are carried out for a signal of another type than the signal on which the correction is applied later on.
- a later signal, on which said Discrete Fourier Transformation having a restricted word length is intended to be applied is not available that easy, but another signal having the known characteristics is easily available.
- said correction is made in connection with said subsequent transformation of signals after applying said subsequent Discrete Fourier Transformation on the signal in question.
- This is a possible way to proceed for obtaining an error corrected signal, and it may easily be realised through suitable means.
- a calculation of such an error corrected inverse transform may for sure require some resources, but the result of the subsequent Discrete Fourier Transformation of a signal will in return be directly error corrected.
- said signals are formed before said Discrete Fourier Transformation by applying analog/digital-conversion on analog signals, which most often will be necessary, since the signals to be processed are most often present in analog form.
- a Discrete Fourier Transformation having a restricted word length is carried out according to the Cooley-Turkey-algorithm , which has done well for Discrete Fourier Transformation having a restricted word length .
- said plurality of samples in step a) is higher than 200, preferably higher than 400.
- Such a high number of samples makes said mean value formation give a reliable result for obtaining an op- timum error correction.
- said subsequent Fourier Transformation is made for applying a frequency analysis on the signal and it is carried out for a signal obtained by transmitting a signal having a frequency varying over time from a moving object and receiving it after it has been reflected from a stationary object and then using it for forming said frequency signal having a frequency being equal to the frequency difference between a signal transmitted and received at a given moment and by that a measure of the instantaneous distance between the object moving and said stationary object.
- the invention has turned out to be particularly well applicable to exactly this type of signal processing and enables a reliable determination of the distance in question within a considerably larger measuring range than without such error correction.
- Fig 1 is a block diagram illustrating how the signal processing through a device according to a preferred embodiment of the invention is carried out
- Fig 2 and 3 are two very simplified block diagrams illustrating the function of devices according to two different preferred embodiments of the invention.
- Fig 4 and 5 are graphs illustrating the differences of the results of a Discrete Fourier Transformation having a restricted word length without and with an error correction according to the invention, respectively, and an ideal result of a Fourier Transformation of the signal in question,
- Fig 6 illustrates schematically a conceivable application of the method and the device according to the invention
- Fig 7 illustrates how the frequency develops over the time for transmitted and received signal of the device according to fig 6
- Fig 8 and 9 illustrate the signal strength with respect to the frequency of signals upon which Discrete Fourier Transformation having a restricted word length is applied in the application according to fig 6 with error correction with respect to a not error corrected signal.
- FIG. 1 It is schematically illustrated in fig 1 how a signal processing in the form of a Discrete Fourier Transformation having a restricted word length is carried out and how a correction of errors occurring as a consequence of the restricted word length is carried out according to the invention in connection therewith.
- An analogue signal having different frequency components intended to be exerted to a frequency analysis arrives to an analog/digital- converter 1 where it is converted into a 8 bit digital signal. This arrives then to a so called 8 bit Hanning-window 2, where a digital filtering takes place, which in principal means a multiplication of the signal by given weight factors.
- the signal is then sent further and 64 samples are taken at 3, on which then in a unit 4 a Discrete Fourier Transformation having a restricted word length is applied, for example according to the Cooley- Turkey-algorithm with the base 4 and 8-10 bit. This is to be compared with a full word length of 16 bit.
- the signal coming out from the unit 4 is the result of a Discrete Fourier Transformation having a restricted word length of a digital signal having an inherent truncating error depending upon said restricted word length .
- the DFT Discrete Fourier Transformation
- N 64 in this case.
- Error coefficients are first of all calculated in such a way that a number (higher than 400) sequences of Gauss noise DFT is calculated and added to each other phase correctly. These error coefficients are thereafter subtracted at 5, in which the out sig- nal from 5 is a corrected DFT. Subsequent signal processing consists in this case of an additional Hanning window 7 and an ideal DFT 6.
- a device of this type is schematically illustrated in fig 2, where the box 8 is a summary for 1 -4 in fig 1 .
- a calculation of a mean value of the results of the Discrete Fourier Transformations carried out for many samples of signals is made at 5 and the mean value calculated is compared with a known ideal value for a result of a said transformation of the signal without making any systematical errors emanating from the restricted word length.
- Once the comparison has been made it is determined in 5 how future results of subsequent Discrete Fourier Transformations having a restricted word length of signals in the box 8 are to be error corrected, and this error cor- rection is introduced after the very Fourier Transformation has taken place in the box 8 at 9.
- the connection 10 between the signal output and the registration and error correction calculating unit 5 is in the practice switched off once the error correction asked for has been determined.
- fig 4 The strength of different frequency components is illustrated in fig 4, in which 14 shows the signal to which the Discrete Fourier Transformation having a restricted word length is applied and 1 5 is a power spectrum related to an ideal DFT. This is to be compared with fig 5, where the signal 15 is also drawn up, but where the signal 16 has been obtained by carrying out the signal processing with error correction according to the invention in connection with the Discrete Fourier Transformation. It appears that at lower frequency components a considerable rimpedement of the error corrected curve 16 to the ideal curve 15 was possible, which means that the signal dynamic has become larger.
- FIG. 6 A conceivable application of a device according to a preferred embodiment of the invention is illustrated in fig 6 and 7, in which an object 17 moves and transmits through a transmitter 1 8 signals having a frequency f varying over the time t according to what is shown in fig 7.
- These analogue signals are reflected by a stationary object 19 and the reflected signal is received by a receiver 20 of the moveabie object, whereupon a signal processing in the form of Discrete Fourier Transformation having a restricted word length with error correction according to the invention is applied on this signal for carrying out a frequency analysis of the signal.
- the signal transmitted by the transmitter 18 at a determined instant is compared with a signal received at the same instant by the receiver 20, and the signals will then have different freque ncies, as illustrated through the arrow 21 in fig 7, and this frequency difference will be directly dependent upon the distance between the object 17 and the object 19.
- a certain noise may leak over from the transmitter 18 to the receiver 20, as indicated through the dashed line 21 . This noise will result in a difference signal having a comparatively low frequency, and when the object 17 arrives sufficiently close to the object 1 9 this leakage will seriously disturb the signal actually reflected from the object 1 9.
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Discrete Mathematics (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Radar Systems Or Details Thereof (AREA)
- Complex Calculations (AREA)
Abstract
Description
Claims
Priority Applications (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AU2001228937A AU2001228937A1 (en) | 2000-01-19 | 2000-12-21 | A method and a device for signal processing |
EP00993799A EP1248994A1 (en) | 2000-01-19 | 2000-12-21 | A method and a device for signal processing |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
SE0000146A SE515642C2 (en) | 2000-01-19 | 2000-01-19 | Method and apparatus for signal processing by means of a Discrete Fourier transform with limited word length |
SE0000146-1 | 2000-01-19 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2001053981A1 true WO2001053981A1 (en) | 2001-07-26 |
Family
ID=20278146
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/SE2000/002627 WO2001053981A1 (en) | 2000-01-19 | 2000-12-21 | A method and a device for signal processing |
Country Status (4)
Country | Link |
---|---|
EP (1) | EP1248994A1 (en) |
AU (1) | AU2001228937A1 (en) |
SE (1) | SE515642C2 (en) |
WO (1) | WO2001053981A1 (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2008128918A1 (en) * | 2007-04-20 | 2008-10-30 | Siemens Aktiengesellschaft | Control arrangement with correction means for systematic position-dependent errors |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5109417A (en) * | 1989-01-27 | 1992-04-28 | Dolby Laboratories Licensing Corporation | Low bit rate transform coder, decoder, and encoder/decoder for high-quality audio |
US5553623A (en) * | 1993-03-12 | 1996-09-10 | Hewlett-Packard Company | Method for calibrating a system for recording and playing back ECG signals |
-
2000
- 2000-01-19 SE SE0000146A patent/SE515642C2/en not_active IP Right Cessation
- 2000-12-21 EP EP00993799A patent/EP1248994A1/en not_active Withdrawn
- 2000-12-21 WO PCT/SE2000/002627 patent/WO2001053981A1/en active Application Filing
- 2000-12-21 AU AU2001228937A patent/AU2001228937A1/en not_active Abandoned
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5109417A (en) * | 1989-01-27 | 1992-04-28 | Dolby Laboratories Licensing Corporation | Low bit rate transform coder, decoder, and encoder/decoder for high-quality audio |
US5553623A (en) * | 1993-03-12 | 1996-09-10 | Hewlett-Packard Company | Method for calibrating a system for recording and playing back ECG signals |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2008128918A1 (en) * | 2007-04-20 | 2008-10-30 | Siemens Aktiengesellschaft | Control arrangement with correction means for systematic position-dependent errors |
US8295973B2 (en) | 2007-04-20 | 2012-10-23 | Siemens Aktiengesellschaft | Control arrangement with correction means for systematic position-dependent errors |
Also Published As
Publication number | Publication date |
---|---|
SE515642C2 (en) | 2001-09-17 |
SE0000146D0 (en) | 2000-01-19 |
SE0000146L (en) | 2001-07-20 |
EP1248994A1 (en) | 2002-10-16 |
AU2001228937A1 (en) | 2001-07-31 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US4763105A (en) | Interleaved digitizer array with calibrated sample timing | |
US5371760A (en) | Method and apparatus for measuring the impulse response of a radio channel | |
US6437578B1 (en) | Cable loss correction of distance to fault and time domain reflectometer measurements | |
US7161511B2 (en) | Linearization system and method | |
US20110129023A1 (en) | Wireless ranging system and related methods | |
CN1968161A (en) | Filter equalization using magnitude measurement data | |
Sujbert et al. | An observer-based adaptive fourier analysis [tips & tricks] | |
US20020065621A1 (en) | Method and apparatus for characterizing frequency response on an error performance analyzer | |
US7460618B2 (en) | System and method for obtaining accurate symbol rate and carrier phase, frequency, and timing acquisition for minimum shift keyed waveform | |
CN109682492B (en) | Frequency estimation method based on frequency domain Gaussian fitting | |
US20050063323A1 (en) | Method and circuit arrangement for determination of transmission parameters | |
EP1248994A1 (en) | A method and a device for signal processing | |
Andria et al. | Interpolated smoothed pseudo Wigner-Ville distribution for accurate spectrum analysis | |
CN112883787B (en) | Short sample low-frequency sinusoidal signal parameter estimation method based on spectrum matching | |
US5555507A (en) | Method for detecting non-linear behavior in a digital data transmission path to be examined | |
Qin et al. | The order tracking of rotating machinery based on instantaneous frequency estimation | |
CN105282086A (en) | Double-tone quadrature measuring method for frequency conversion system group delay | |
US10735036B1 (en) | Method for measuring frequency offset between an RF transmitter and a test receiver | |
JP2003319015A (en) | Multi-functional measuring system and waveform measuring method | |
Ferrero et al. | A new approach to the Fourier analysis of periodic signals for the minimization of the phase errors | |
Liguori | Uncertainty on signal parameter estimation in frequency domain | |
US20230388154A1 (en) | Vector channel analyzer | |
JPH07245634A (en) | Method and system for description of characteristic of phase-modulated signal | |
Ferrero et al. | A fast frequency-domain interpolation method for the evaluation of the frequency and amplitude of spectral components | |
EP0882994A1 (en) | Method and device for the characterization of a network |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AK | Designated states |
Kind code of ref document: A1 Designated state(s): AE AG AL AM AT AU AZ BA BB BG BR BY BZ CA CH CN CR CU CZ CZ DE DE DK DK DM DZ EE ES FI FI GB GD GE GH GM HR HU ID IL IN IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MA MD MG MK MN MW MX MZ NO NZ PL PT RO RU SD SE SG SI SK SK SL TJ TM TR TT TZ UA UG US UZ VN YU ZA ZW |
|
AL | Designated countries for regional patents |
Kind code of ref document: A1 Designated state(s): GH GM KE LS MW MZ SD SL SZ TZ UG ZW AM AZ BY KG KZ MD RU TJ TM AT BE CH CY DE DK ES FI FR GB GR IE IT LU MC NL PT SE TR BF BJ CF CG CI CM GA GN GW ML MR NE SN TD TG |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application | ||
DFPE | Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101) | ||
REEP | Request for entry into the european phase |
Ref document number: 2000993799 Country of ref document: EP |
|
WWE | Wipo information: entry into national phase |
Ref document number: 2000993799 Country of ref document: EP |
|
WWP | Wipo information: published in national office |
Ref document number: 2000993799 Country of ref document: EP |
|
REG | Reference to national code |
Ref country code: DE Ref legal event code: 8642 |
|
NENP | Non-entry into the national phase |
Ref country code: JP |