US3800131A - Hilbert transformer - Google Patents

Hilbert transformer Download PDF

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Publication number
US3800131A
US3800131A US00238213A US23821372A US3800131A US 3800131 A US3800131 A US 3800131A US 00238213 A US00238213 A US 00238213A US 23821372 A US23821372 A US 23821372A US 3800131 A US3800131 A US 3800131A
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signal
multiplier
combining
interim
input signal
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Expired - Lifetime
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US00238213A
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English (en)
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S White
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Boeing North American Inc
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North American Rockwell Corp
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Priority to US00238213A priority Critical patent/US3800131A/en
Priority to CA155,560A priority patent/CA979078A/en
Priority to GB5425072A priority patent/GB1405168A/en
Priority to DE2302298A priority patent/DE2302298C3/de
Priority to FR7302116A priority patent/FR2177725A1/fr
Priority to JP48017015A priority patent/JPS4915339A/ja
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Publication of US3800131A publication Critical patent/US3800131A/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/19—Arrangements for performing computing operations, e.g. operational amplifiers for forming integrals of products, e.g. Fourier integrals, Laplace integrals, correlation integrals; for analysis or synthesis of functions using orthogonal functions
    • G06G7/1942—Arrangements for performing computing operations, e.g. operational amplifiers for forming integrals of products, e.g. Fourier integrals, Laplace integrals, correlation integrals; for analysis or synthesis of functions using orthogonal functions for forming other integrals of product, e.g. orthogonal functions, Laplace, Laguerre, Walsh, Hadamard, Hilbert
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0211—Frequency selective networks using specific transformation algorithms, e.g. WALSH functions, Fermat transforms, Mersenne transforms, polynomial transforms, Hilbert transforms

Definitions

  • the present inventive transformer is comprised of a first and second channel with the first channel transforming an input signal by a desired function and providing as an output the transformed input signal.
  • a second channel transforms the input signal by an identical function and provides an output signal which is identical to the output signal from the first channel except that all frequency components of the signal in the second channel are phase shifted by 90 with respect I to the signal in the first channel.
  • This particular type of signal processing is called Hilbert transformation and, in the past, various approximations have been developed for achieving the desired signal relationship
  • the signal information is applied through a bandpass filter to a 90 phase shifter in a first channel to obtain a Hilbert transformer approximation of the bandpass filtered signal at the output of the bandpass filter which is applied to a second Channel.
  • signal information is applied through a digital bandpass filter to a convolution filter which convolves the signal with a ramp voltage to develop a Hilbert transformer approximation of the filtered output signal from the digital bandpass filter which is applied to a second channel.
  • the present invention is directed to a circuit for achieving an exact solution to this problem.
  • the present invention is directed to the field of signal transformers and, more particularly, to a Hilbert transformer.
  • Each of the first multiplier means receives a periodic function signal whose frequency defines the center frequency of the bandpass characteristics of the overall filtering function cosine signal, which signal has a frequency to which is translated the bandpass ofa linear filter (see below).
  • the outputs of the first multiplier means are fed to the inputs of four identical linear filters, respectively.
  • the outputs of these filters are respectively fed to four second multiplier means, which multiplier means also selectively receive the sine and cosine signals for multiplication with the filter output signals.
  • the outputs of the first channel second multiplier means are summed together to provide a transformed signal with the outputs of the second pair of second multiplier means differenced together to provide a second output signal which is transformed in an identical manner as the first signal but shifted in phase by 90.
  • FIG. 1 illustrates in block diagram form the transfer function of a Hilbert transformer
  • FIG. 2 illustrates in schematic and block diagram form the basic circuit used in part to achieve the functions illustrated in FIG. 1;
  • FIG. 3 illustrates one preferred embodiment of the invention in schematic and block diagram form for O achieving the total functions illustrates in FIG. 1;
  • FIG. 4 illustrates in electronic schematic form a circuit which may be used in one of the blocks of FIGS. 2 and 3;
  • FIG. 5 illustrates in block form a digital circuit which may be used as one of the blocks contained in FIGS. 2 and 3.
  • FIG. 1 there is shown an idealized Hilbert transformer 10.
  • the transformer is comprised of two Chan-- nels, one 11 and the other 12.
  • Each channel is comprised of an identical transfer function in this example G(s), which transfer function operates upon an input signal x(t) to yield substantially identical output signals y (t) and y (t), which signals have each frequency component shifted with respect to each other.
  • FIG. 2 one channel of implementation of the present transformer is shown.
  • the input signal x(t) is fed to multipliers l5 and 16. These multipliers also receive signals A and C, which signals will be defined below.
  • the outputs of the multipliers are designated x and x respectively. These outputs are fed to linear filters 17 and 18 which, for example, may be lowpass filters.
  • the outputs of filters l7 and 18 are designated x and x respectively, and are fed to multipliers l9 and 20, respectively.
  • Multiplier 19 also receives a signal B for multiplication with the signal x
  • Multiplier 20 receives a signal D for multiplication with signal x
  • the output of multiplier 19 is designated x with the output of multiplier 20 being designated x
  • Both of these outputs are provided to combining means 21 to provide an output signal x indicative of the difference between signals x and x.
  • the signals A, B, C and D are defined as periodic function signals where:
  • iAMia-m.)1xija-till als1 X (jw) may be obtained from X fiw) and X fljw) obtained from X fiw) by replacing A and B by C, and
  • FIG. 3 an embodiment of the Hilbert transformer is shown.
  • the channels are identical in construction to the channel shown in FIG. 2 except for the inputs to the multipliers and the signs of the signals feeding the output combiners.
  • multipliers 25 and 27 receive the reference signal sin (0,1, while multipliers 26 and 28 receive the reference signal cos am.
  • multipliers 16a and 19a receive the reference signal cos an! and multipliers a and 20a receive the reference signal sin w,t.
  • the outputs from multipliers 27 and 28 are summed together in combiner 29 to provide the output signal Y,( 'w), while the difference output from combiner 21a provides the signal y g'w).
  • the signal frequency components at the output of channel 12 are shifted 90 in phase with respect to the signal frequecy components from channel 11, but, otherwise, each of the signals have undergone the same transformation.
  • the transformation blocks labeled 17 and 18, 17a and 18a, and 17b and 18b, are generally shown and can be varied to fit specific applications.
  • One specific application, analog in form, is shown in FIG. 4 as a simple R-C filter.
  • the circuit is shown of a summing means 30 receiving as one input the input to the digital filters and the other input, the output of a multiplier 31 having a gain A.
  • the output of the summing means 30 is the digital filters output, which output additionally is fed to a delay means 32 whose output is fed to a substraction means 33.
  • substraction means 33 subtracts from the delayed signal from delay 32 the presently received input to the digital filter.
  • the output of substraction means 33 is fed to the input of the multiplier 31.
  • a Hilbert transformer system for transforming an input signal to provide first and second output signals respectively having frequency components phase shifted with respect to each other, the system comprising:
  • a first channel comprised of first and second linear first and second multiplier means having their outputs connected to the inputs of said first and second linear filters, respectively;
  • third and fourth multiplier means for receiving the outputs of said first and said second linear filters respectively, said first and second multiplier means having as inputs said input signal, said first and third multiplier means having as inputs a first sinusoidal signal, and said second and fourth multiplier means having as inputs a second sinusoidal signal, said first and second sinusoidal signals having a frequency proportional to a desired frequency translation;
  • summing means for receiving the formed product from said third and fourth multiplier means and providing a first output signal
  • a second channel comprised of third and fourth lin ear filters, fifth and sixth multiplier means having their outputs connected to the inputs of said third and fourth linear filters respectively, seventh and eighth multiplier means for receiving the outputs of said third and fourth linear filters respectively, said fifth and sixth multiplier means having as inputs said input signal, said fifth and eighth multiplier means having as inputs said first sinusoidal signal, and said sixth and seventh multiplier means having as inputs said second sinusoidal signal; and
  • subtraction means for receiving the formed product from said seventh and eighth multiplier means and providing a second output signal each frequency component of which is shifted 90 in phase from the respective frequency components of said first output signal.
  • a method employing first and second signals in mutual phase quadrature for automatically transforming an input signal into first and second output signals which comprises the steps of:
  • a Hilbert transformation system comprising:
  • first means being responsive to an input signal and a first reference signal for developing a first transformed signal
  • first and second means being responsive to the input signal and a second reference signal for developing a second transformed signal
  • the first and second referfirst combining means being responsive to the first and third product signals for providing a first output signal having first frequency components
  • second combining means being responsive to the second and fourth product signals for providing a second output signal having second frequency components which are shifted in phase by from the respective frequency components of the first signal.
  • said first means includes fifth multiplier means responsive to the input signal and the first reference signal for developing a fifth product signal, and a first linear filter for developing the first transfer function in response to the fifth product signal; and
  • said second means includes sixth multiplier means responsive to the input signal and the second reference signal for developing a sixth product signal, and a second linear filter for developing the second transfer function in response to the sixth product signal.
  • said first means further includes seventh multiplier means responsive to the input signal and the first reference signal for developing a seventh product signal, and a third linear filter coupled between said seventh and second multiplier means for developing and applying the first transformed signal to said second multiplier means in response to the seventh product signal, said first linear filter in said first means being coupled to said first multiplier means; and
  • said second means further includes eighth multiplier means responsive to the input signal and the second reference signal for developing an eighth product signal, and a fourth linear filter coupled between said eighth and fourth multiplier means for developing and applying the second transformed signal to said fourth multiplier means in response to the eighth product signal, said second linear filter in said second means being coupled to said third multiplier means.
  • Colwmn 3 lino MO, add on equals sign between "1'5" and "sihw t";

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  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • General Physics & Mathematics (AREA)
  • Software Systems (AREA)
  • Algebra (AREA)
  • Computing Systems (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Amplitude Modulation (AREA)
  • Networks Using Active Elements (AREA)
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US00238213A 1972-03-27 1972-03-27 Hilbert transformer Expired - Lifetime US3800131A (en)

Priority Applications (6)

Application Number Priority Date Filing Date Title
US00238213A US3800131A (en) 1972-03-27 1972-03-27 Hilbert transformer
CA155,560A CA979078A (en) 1972-03-27 1972-10-31 Hilbert transformer
GB5425072A GB1405168A (en) 1972-03-27 1972-11-23 Hiblert transformation system
DE2302298A DE2302298C3 (de) 1972-03-27 1973-01-18 Hilbertumsetzer
FR7302116A FR2177725A1 (fr) 1972-03-27 1973-01-22
JP48017015A JPS4915339A (fr) 1972-03-27 1973-02-09

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US00238213A US3800131A (en) 1972-03-27 1972-03-27 Hilbert transformer

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US3800131A true US3800131A (en) 1974-03-26

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US (1) US3800131A (fr)
JP (1) JPS4915339A (fr)
CA (1) CA979078A (fr)
DE (1) DE2302298C3 (fr)
FR (1) FR2177725A1 (fr)
GB (1) GB1405168A (fr)

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3908114A (en) * 1974-08-12 1975-09-23 Rockwell International Corp Digital Hilbert transformation system
US4287418A (en) * 1978-07-06 1981-09-01 Divin Jury Y Method for measuring the spectral distribution of electromagnetic radiation intensity and spectrometer of millimetric and far-infrared ranges for effecting same
WO1982000226A1 (fr) * 1980-07-02 1982-01-21 Inc Motorola Systeme de modulation de transformation
US4462114A (en) * 1980-07-02 1984-07-24 Motorola, Inc. Signum signal generator
US4509135A (en) * 1980-07-02 1985-04-02 Motorola, Inc. Cosine signal correction circuit
US4803739A (en) * 1984-12-10 1989-02-07 Nippon Telegraph And Telegraph Corporation SSB communication system
US4967161A (en) * 1988-08-24 1990-10-30 Hitachi, Ltd. Signal processing method and apparatus

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3830729C2 (de) * 1988-09-09 1998-04-09 Hagenuk Marinekommunikation Gm Verfahren zum Erzeugen eines Einseitenbandsignals und Schaltungsanordnung zur Durchführung des Verfahrens
DE4210069A1 (de) * 1992-03-27 1993-09-30 Asea Brown Boveri Amplitudenmodulierter Rundfunksender für verschiedene Modulationsarten, insbesondere DSB, SSB und ISB

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2020409A (en) * 1933-08-15 1935-11-12 American Telephone & Telegraph Band separation system
US2605396A (en) * 1949-01-21 1952-07-29 Westinghouse Electric Corp Frequency selective device
US3259692A (en) * 1960-10-26 1966-07-05 Communications Patents Ltd Multi-channel electric wave signalling apparatus
FR1560930A (fr) * 1967-04-25 1969-03-21
US3548210A (en) * 1965-08-30 1970-12-15 Bendix Corp Automatic stereoplotter
US3585529A (en) * 1968-11-18 1971-06-15 Bell Telephone Labor Inc Single-sideband modulator
US3621388A (en) * 1968-11-04 1971-11-16 Spectral Dynamics Corp Electronic wave analyzer for determining the frequency and amplitude of components in a complex waveform

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2020409A (en) * 1933-08-15 1935-11-12 American Telephone & Telegraph Band separation system
US2605396A (en) * 1949-01-21 1952-07-29 Westinghouse Electric Corp Frequency selective device
US3259692A (en) * 1960-10-26 1966-07-05 Communications Patents Ltd Multi-channel electric wave signalling apparatus
US3548210A (en) * 1965-08-30 1970-12-15 Bendix Corp Automatic stereoplotter
FR1560930A (fr) * 1967-04-25 1969-03-21
US3621388A (en) * 1968-11-04 1971-11-16 Spectral Dynamics Corp Electronic wave analyzer for determining the frequency and amplitude of components in a complex waveform
US3585529A (en) * 1968-11-18 1971-06-15 Bell Telephone Labor Inc Single-sideband modulator

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Chang et al.: Passive N Path Filter Realisation Electronics Letters Vol. 7, No. 12 June 1971 p. 349/351. *
Cowley: An Active Filter for the Measurement of Process Dynamics. Instr. Society of America Proceedings of the 19th Annual ISA Conference Vol. 19 Oct. 12 15, 1964, New York part in 3.2 3 64 pages 1 5 and 9 11. *
G. DiPillo: On the Analogue Methods for Power Spectral Density Estimation Int. Journal of Control Vol. 11, No. 5, May 1970 p. 759 770. *
Weaver: A Third Method of Generation and Detection of Single Sideband Signals; Proceed. IRE Dec. 1956, pages 1703 to 1705. *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3908114A (en) * 1974-08-12 1975-09-23 Rockwell International Corp Digital Hilbert transformation system
US4287418A (en) * 1978-07-06 1981-09-01 Divin Jury Y Method for measuring the spectral distribution of electromagnetic radiation intensity and spectrometer of millimetric and far-infrared ranges for effecting same
WO1982000226A1 (fr) * 1980-07-02 1982-01-21 Inc Motorola Systeme de modulation de transformation
US4462114A (en) * 1980-07-02 1984-07-24 Motorola, Inc. Signum signal generator
US4509135A (en) * 1980-07-02 1985-04-02 Motorola, Inc. Cosine signal correction circuit
US4525862A (en) * 1980-07-02 1985-06-25 Motorola, Inc. Transform modulation system
US4803739A (en) * 1984-12-10 1989-02-07 Nippon Telegraph And Telegraph Corporation SSB communication system
US4967161A (en) * 1988-08-24 1990-10-30 Hitachi, Ltd. Signal processing method and apparatus

Also Published As

Publication number Publication date
JPS4915339A (fr) 1974-02-09
FR2177725A1 (fr) 1973-11-09
GB1405168A (en) 1975-09-03
DE2302298A1 (de) 1973-10-11
DE2302298B2 (de) 1974-03-28
DE2302298C3 (de) 1974-10-24
CA979078A (en) 1975-12-02

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