US3800131A

US3800131A - Hilbert transformer

Info

Publication number: US3800131A
Application number: US00238213A
Authority: US
Inventors: S White
Original assignee: North American Rockwell Corp
Current assignee: Boeing North American Inc
Priority date: 1972-03-27
Filing date: 1972-03-27
Publication date: 1974-03-26
Anticipated expiration: 1991-03-26
Also published as: GB1405168A; JPS4915339A; CA979078A; DE2302298A1; DE2302298C3; FR2177725A1; DE2302298B2

Abstract

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 to the signal in the first channel.

Description

United States Patent 1191 White [4 1 Mar. 26, 1974 HILBERT TRANSFORMER [75] Inventor: Stanley A. White, Yorba Linda,

Calif.

[73] Assignee: North American Rockwell Corporation, El Segundo, Calif.

[22] Filed: Mar. 27, 1972 [21] Appl. No.: 238,213

[52] US. Cl. 235/197, 179/15 BC, 325/60,

332/23 [51] Int. Cl G06g 7/26 [58] Field of Search 235/197, 194, 193, 189,

235/150, 53, I86, 181; 332/23, 41, 45, 48; 179/15 BC; 325/60, 137

[56] References Cited UNITED STATES PATENTS 3,548,210 12/1970 Chapelle et al 250/202 2,020,409 11/1935 Green 332/45 2,605,396 7/1952 Cheek 332/45 3,259,692 7/1966 Aspinwall 332/45 3,585,529 6/1971 Darlington 332/45 3,621,388 1l/1971 Davis 235/181 FOREIGN PATENTS OR APPLICATIONS 1,560,930 3/1969 France OTHER PUBLICATIONS Cowley: An Active Filter for the Measurement of Pro- 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.

Primary ExaminerFelix D. Gruber Attorney, Agent, or Firm-Rolf M. Pitts; I-I. Fredrick Hamann; L. Lee Humphries [5 7 ABSTRACT 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.

5 Claims, 5 Drawing Figures 1 I H w) 1 I i 25 27 l x111 I 29 I t I 6 zs\ wy -xuw)%fiiw i i|+nfliww fl ll/ 1 l 1 Ho I l L "a osws' cos (n 1 l i i i H w l r I l i 1 15a 19a I I l 2 /'i m mum-[x11 1 n[m-w.1]-H [wow] l2 2 1 i M (1m) I 161 L i J SHEEI 3 BF 3 INPUT FIG.5

HILBERT TRANSFORMER BACKGROUND OF THE INVENTION In the field of communications systems, designs that incorporate filters which process information through two channels in a particular fashion are frequently called for. The information in only one channel is shaped by some specified transfer function, frequently a narrow-band filter. In addition, each frequency component of the signal in the first channel is phase shifted by 90 with respect to the signal in the second 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 In one type of prior art system, 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. In a second type of prior art system, 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.

SUMMARY OF THE INVENTION The present invention is directed to the field of signal transformers and, more particularly, to a Hilbert transformer. In one preferred embodiment of the invention, there are provided two channels with each channel having a pair of first multiplier means for receiving an input signal. 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.

It is, therefore, an object of the present invention to provide an improved signal transformer.

It is another object of the present invention to provide a signal transformer wherein the signals are transformed in an identical manner but shifted in phase exactly 90.

These and other objects of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein like characters indicate like parts and which drawings form a part of this invention.

BRIEF DESCRIPTION OF THE DRAWINGS 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; and

FIG. 5 illustrates in block form a digital circuit which may be used as one of the blocks contained in FIGS. 2 and 3.

DESCRIPTION OF THE PREFERRED EMBODIMENTS In 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.

In 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:

A: 2 A jnw t n: so

and B, C, and D are similarly defined. Defining the Fourier transform of the signal x as:

F I k( )l kU The Fourier transforms of the signals X 1 to X, are therefore given below:

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

Select all m n only i.e., set 8,, B to eliminate modulation products of X:

Two interesting forms are immediately obvious:

I. set A, B A B H2] and C, D C. D 1/2 all others zero which makes Hi(j l l/'( n)l+ L/( dll Therefore A=B sin w,,t; C=D=cos w t. This transformation takes a filter response and moves it up to a higher frequency, such as making a lowpass filter into a bandpass filter.

2. set A, -A-, -D, l/2j and B, B

C CL, l/2 all others zero which makes In 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. In channel 11,

multipliers

25 and 27 receive the reference signal sin (0,1, while

multipliers

26 and 28 receive the reference signal cos am. In channel 12, 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). In mathematically comparing the signals y, to y it can be seen that 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.

In the FIGS. 2 and 3, 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. In this application, the transfer function Hg'w) equals a divided by jw-l-a. If the same transfer function is to be digital in form, then the circuit of FIG. 5 can be used wherein where A e T= Sampling interval 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.

What has been shown in the preceding description is a Hilbert transformer which is generalized in nature and can be used with any desired transfer function HU'w).

While there has been shown what is considered to be the preferred embodiment of the invention, it will be manifest that many changes and modifications may be made therein without departing from the essential spirit of the invention. It is intended, therefore, in the annexed claims, to cover all such changes and modifications as fall within the true scope of the invention.

What is claimed is:

1. 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.

2. 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:

combining the first signal with said input signal in a first multiplier;

transforming the combination of said first signal and said input signal by means of a first filter circuit into a first interim transformed signal;

combining said first interim transformed signal with said first signal in a second multiplier to develop a first interim output signal; combining the second signal with said input signal in a third multiplier;

transforming the combination of said second signal and said input signal in a second filter circuit into a second interim transformed signal;

combining said second interim transformed signal with said second signal in a fourth multiplier to develop a second interim output signal;

combining said first and second interim output signals in a first combining circuit to develop said first output signal;

combining said first signal with said input signal in a fifth multiplier; transforming the combination of said first signal and said input signal by means of a third filter circuit into the first interim transformed signal;

combining said first interim transformed signal with said second signal in a sixth multiplier to develop a third interim output signal;

combining said second signal with said input signal in a seventh multiplier;

transforming the combination of said second signal and said input signal by means ofa fourth filter circuit into the second interim transformed signal;

combining said second interim transformed signal with said first signal in an eighth multiplier to develop a fourth interim output signal; and

combining said third and fourth interim output signals in a second combining circuit to develop the second output signal which has frequency components that are substantially 90 out of phase with respect to respective associated frequency components of said first output signal.

3. A Hilbert transformation system comprising:

first means being responsive to an input signal and a first reference signal for developing a first transformed signal;

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.

4. The system of claim 3 wherein:

' 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.

5. The system of claim 4 wherein:

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.

"M050 UNETED STATES fit PERT ()FHCE (s/ss) v ClLRTle with 01-? CORRECEiGN Patent No. 3 800, 1.31. l mrch P6, lfl 'fh Inventor(s) Stanley A. White Page 1 0T3 .It is certified that error appears in the aboveddentiiied patent and that said Letters Patent are hereby corrected as shown below:

E FIG. 2, 'change the reference numeral for the multiplier'that receives the X signal from "2 to --20--.

In FIG. 3 (which is also the abstracted drawing),

output ef the ccmbiner 29 from:

"y (fi (Jw) 2 3(00 60 H {3(a) 1 w) (Jcu)' Uw) {eh-1(0) 40 Exp- (a m5] L L change the equation at the output of the combiner 21a F -g: X JLO j H 'l( (I) I H 3(0) we) if" change the equation at the designate the upper block entitled HLjQJ)" in channel ll by the reference numeral --lT'b--; and designate the lower block entitled "H(jw)." in channe by the reference numeral --l8b--.

In FIG. delete the legend "R and to the right of the dashed block add the legend -RC "3 In FIG. 5, the block entitled .A" should be designated by the reference numeral "31; and the reference numeral "32 should be added immediately to the right of the legend "DELAY" Column 1, lines rlfi delete "cosine signal, which signal. hat: a frequency to which is translated the bandpass of a linear filter (see below)" Column 3, line 28, after "D j" insert and;

Patent N QQW'U, '51. MM M DHLOIJ il 'ILQQ LQ{ Pvt-"inlay A. White Page 5 oil 2 It is certified that. error Pppmnff: in the -fbOVP-*id'.l"jif'lCd patent and that; said Letters: Patent arc hczicby corrected as shown below:

Colwmn 3, lino MO, add on equals sign between "1'5" and "sihw t";

Column 3, line 61, change y; to Y Column 3, line 65, change "frequecy to ---frequency--; (301mm 4, line 9, change "A to "A Colzunn I}, 1|..inc 10, change "e to --e" Column 4, lino 11, after "shown" insert. --comprisnd--=;

Column line 12, change "filters" to --filter---:

Column line 16, change "substrac'ti.on to --subtract ion- Column line 1?, charge "Substraccion" to --Subtraction---;-

Coir-um. line 19, change "substrac'tion" to --subtraction--.

Signed and sealed this 1st day of October 1974.

(SEAL) Attest:

MCCOY MQGIBSON R; c0 MARSHALL DANN. Attesting Officer 1. Commissioner of Patents

Claims

1. A Hilbert transformer system for transforming an input signal to provide first and second output signals respectively having frequency components phase shifted 90* with respect to each other, the system comprising: a first channel comprised of first and second linear filters; 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 linear 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.

2. 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: combining the first signal with said input signal in a first multiplier; transforming the combination of said first signal and said input signal by means of a first filter circuit into a first interim transformed signal; combining said first interim transformed signal with said first signal in a second multiplier to develop a first interim output signal; combining the second signal with said input signal in a third multiplier; transforming the combination of said second signal and said input signal in a second filter circuit into a second interim transformed signal; combining said second interim transformed signal with said second signal in a fourth multiplier to develop a second interim output signal; combining said first and second interim output signals in a first combining circuit to develop said first output signal; combining said first signal with said input signal in a fifth multiplier; transforming the combination of said first signal and said input signal by means of a third filter circuit into the first interim transformed signal; combining said first interim transformed signal with said second signal in a sixth multiplier to develop a third interim output signal; combining said second signal with said input signal in a seventh multiplier; transforming the combination of said second signal and said inpuT signal by means of a fourth filter circuit into the second interim transformed signal; combining said second interim transformed signal with said first signal in an eighth multiplier to develop a fourth interim output signal; and combining said third and fourth interim output signals in a second combining circuit to develop the second output signal which has frequency components that are substantially 90* out of phase with respect to respective associated frequency components of said first output signal.

3. A Hilbert transformation system comprising: first means being responsive to an input signal and a first reference signal for developing a first transformed signal; second means being responsive to the input signal and a second reference signal for developing a second transformed signal, the first and second reference signals being in mutual phase quadrature with each other; first and second multiplier means, coupled to said first means, being responsive to the first transformed signal and to the respective reception of the first and second reference signals for respectively developing first and second product signals; third and fourth multiplier means, coupled to said second means, being responsive to the second transformed signal and to the respective reception of the second and first reference signals for respectively developing third and fourth product signals; first 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 90* from the respective frequency components of the first signal.

4. The system of claim 3 wherein: 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.

5. The system of claim 4 wherein: 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.