METHODS AND SYSTEMS FOR DESIGNING AND MAKING SIGNAL-PROCESSOR CIRCUITS WITH INTERNAL COMPANDING, AND THE RESULTING CIRCUITS

Abstract: Electrical filter or signal processor circuits are provided with internal companding for reduced sensitivity to noise while input-output response is as conventionally specified. In the continuous-time case, for a specified circuit described by state equations with a state vector x(t), state equations are derived of an equivalent companding circuit having a state vector w(t)=G(t) x(t), where G(t) is a suitably chosen matrix (12). G(t) may be chosen for instantaneous or syllabic companding of the state vector. A corresponding technique applies to discrete-time circuits.

Description: Description Methods And Systems For Designing And Making Signal-Processor Circuits With Internal Companding, And The Resulting Circuits Background of the Invention The invention relates to companding, i.e., the compression and expansion of the dynamic range of electrical signals. In companding, an input signal is compressed so that the dynamic range of the compressed signal is reduced as compared with the input signal. After desired transmission or processing, the dynamic range of the signal is expanded. Noise picked up in transmission or processing then has reduced amplitude. Companding may be considered as originating in the field of telephone signal transmission. It is also used in acoustical recording and playback, where so- called Dolby systems and the like have found widespread use in high-fidelity reproduction. Such systems can reproduce sound with reduced noise. Companding is being used in other devices, such as hearing aids, for example, where power consumption must be minimized. Low-power devices are particularly susceptible to noise. Such concerns also apply generally to today's integrated circuits, which usually must operate with small voltage swings and thus are vulnerable to noise. This is true especially of high-Q filters, in which large internal gains can amplify noise and interference. The following published items are representative of the state of the art: 1. Y. P. Tsividis et al. , "Companding in Signal Processing", Electronics Letters. Vol. 26 (1990) , pp. 1331-1332; 2. F. Callias et al., "A Set of Four IC's in CMOS Technology for a Programmable Hearing Aid", IEEE Journal of Solid-State Circuits. Vol. 24 (1989), pp. 301-312; 3. E. Seevinck, "Companding Current-mode Integrator: a New Circuit Principle for Continuous-time Monolithic Filters", Electronics Letters. Vol. 26 (1990) , pp. 2046-2047; 4. D. R. Frey, "Log-domain Filtering: an Approach to Current-mode Filtering", IEE Proceedings-G. Vol. 140 (1993), pp. 406-416; 5. E. Dijkstra et al. , "Low-Power Oversampled A/D Converters", in Van de Plassche et al. (eds.), Analog Circuit Design: Low-power Low-voltage. Integrated Filters, and Smart Power. Kluwer, Boston, 1995. Among these items, 3., 4. and 5. are concerned with "instantaneous companding", in which companding is effected based on a signal's instantaneous value. By distinction, items 1. and 2. are concerned with "syllabic companding", depending on some measure of a signals's average strength in a suitably chosen time interval. Of particular present interest in electrical signal processing are filter circuits with companding, and with linear input-output response. Among the above-referenced items, 3. and 4. disclose special cases of such circuits. Quite generally, for a continuous-time linear, time-invariant filter or signal-processor circuit as described by state equations in the standard form x = Ax + Bu and y = Cx + Du where u(t) is the input vector, y(t) the output vector, x(t) the state vector, and A, B, C and D are matrices of appropriate dimensions, it would be desirable to have a technique for producing a circuit with internal companding and with the same input-output response as the specified circuit. Summary of the Invention In the case of a continuous-time filter or signal processor, such a companding circuit can be realized by implementing, instead of the specified circuit, a circuit described by state equations w = Aw + Bu and y = Cw + Du for a derived state vector w(t) = G(t) x(t) of derived state variables, and for matrices = GG' 1 + GAG 1 , B = GB and C = CG "1 , wherein the nonsingular, differentiable matrix G(t) has been determined such that the derived state vector w(t) is companded for reduced noise as compared with the state vector x(t) . It can be verified by substitution that the derived new circuit is input- output equivalent to the originally specified, internally linear circuit. In this description, t denotes time, and a "dot" superposed on a symbol designates taking the derivative with respect to time of the entity denoted by the symbol under the dot. When applied to a vector or a matrix, the derivative is understood component- or element-wise. In the case of a discrete-time filter or signal processor, described by state equations x(n+l) = Ax(n) + Bu(n) and y(n) = Cx(n) + Du(n) where integers n and n+l refer to consecutive instants of discrete time, new circuit matrices are determined by A = G(n+l)AG-'(n), B = G(n+1)B and C = CG "1 (n) . It can be verified by substitution that the derived new circuit is input-output equivalent to the originally specified, internally linear circuit. Brief Description of the Drawing Fig. 1 is a block diagram of a system in accordance with a preferred embodiment of the invention, as may be implemented as a programmed computer, for example. Fig. 2 is a schematic of a companding filter or signal processor circuit made in accordance with a preferred embodiment of the invention. Fig. 3 is a block diagram representing an example of a specified conventional second-order bandpass filter circuit. Fig. 4 is a block diagram of a second-order bandpass filter circuit with companding, made in accordance with an example of the invention based on the circuit of Fig. 3. Figs. 5a-5d are diagrams of waveforms for the companding filter circuit of Fig. 3. Figs. 6a and 6b are diagrams of output current as a function of time, for the conventional filter circuit corresponding of Fig. 3, and for the preferred companding filter circuit of Fig. 4, respectively. Detailed Description of Preferred Embodiments With reference to the Summary above, Fig. 1 shows input means 11 (e.g., a computer keyboard) for entering the coefficients of the matrices A, B, and C representing a filter or signal processor circuit with specified characteristics, means 12 for determining the coefficients of the matrix G (e.g., by trial and error with the goal of internal companding for noise reduction), computing means 13 (e.g., a suitably programmed CPU) for determining the elements of the matrices A, B and C, and output means 14 (e.g., a printer) for the elements of these determined matrices. With the output from the system of Fig. 1, a preferred filter or signal processor circuit 21 with internal companding is as schematically shown in Fig. 2. This circuit has the same input-output characteristics as the specified circuit. Fig. 3 illustrates, as an example, a specified continuous-time second-order bandpass filter circuit with gain elements (e.g., transconductors) 31, 32, 34, 34 and 35, and with integrators 36 and 37. In Fig. 3, a^ denotes the i-j-th element of the matrix A, and correspondingly for the matrices B and C. Fig. 4 shows the circuit of Fig. 3 modified, with gain elements 41-45 and with an additional gain element 46. This additional gain element, as well as the indicated gains of the gain elements 41-45, have been determined as described below, representing an example in accordance with the invention. With the state variables of the circuit of Fig. 3 denoted by x, and x 2 , for an input-output equivalent version with state variables w,(t) = g(t) xj(t) and w 2 (t) = g(t) x,(t) f the 2-by-2 matrix G in this example is chosen to have elements Su = g 2 = 9 and g 12 = g 21 = 0. With these, the new circuit matrices A, B and C are obtained with elements as shown in Fig. 4. For syllabic companding, with g(t) = l/ (η + e u (t)/e 0 ) where e u (t) is an approximation to the envelope of u(t) , e 0 is the envelope level at which zero compression is desired, and η is a small number, used to prevent g from becoming infinite when the input is zero, the resulting circuit was simulated with the circuit simulation program Pspice as a current-input, current-output circuit, and with two capacitors as integrators. Voltage input and output could equally be used. An actual differentiator was used in this example to produce g from g. The parts containing g in Fig. 4 were implemented with controlled sources. A second-order passive filter was required in the envelope detector, to avoid excessive ripple at the input of the differentiator. The design was for a center frequency of 1 kHz, a quality factor of 10, and a peak gain of 1. Values e 0 = 10 nA and η = 0.01 were used. For an input current as shown in Fig. 5a, the output current is shown in Fig. 5b. By comparing this to simulations of the original conventional filter circuit, it has been verified that the output of the two circuits is the same, i.e., there is no envelope distortion introduced by the companding. This would have been impossible if only input and output compressor/expander blocks had been used (e.g., as in items 1. and 2. cited above), since the latter would not take into account the effect of the filter's transfer function on the envelope. The integrator outputs are shown in Figs. 5c and 5d. They are properly compressed at a level chosen to be slightly lower than their saturation value. Thus, distortion is prevented while the internal signals stay well above the noise level. To check the immunity to noise and interference at internal points, pseudo-random noise sources were added in the filter circuit and transient simulations were carried out to catch the effects of companding. For an input of 1 nA peak, the results are shown in Fig. 6a for the conventional filter circuit and in Fig. 6b for the companding filter circuit. As expected from the definition of g(t) and Fig. 4, the input block amplifies the signal to be processed by approximately 20 dB. The output block attenuates the signal, and thus the noise, by the same amount. More generally in a preferred method, for known matrices A, B and C for an original filter or signal processor circuit, the elements g ;j of the matrix G are determined heuristically or methodically for companding. With the matrix G thus defined, the matrices A, B and C are determined, for physical implementation of an input-output equivalent circuit based on the latter matrices. Conveniently, these determinations can be carried out by a suitably programmed computer. The method described can be applied to any filter or signal processor circuit topology which can be described by state equations, including, e.g., the popular "leap-frog" topology. The matrix G can be chosen to depend on instantaneous signal values for instantaneous companding, on average signal strength as in AGC circuits for syllabic companding, or on both. G can be produced from input, output or internal signals (or a combination thereof) of a specified filter or signal processor circuit, or of a companion circuit (e.g., a replica of the specified circuit with scaled signals) . Such options apply correspondingly to discrete- ime circuits, e.g., switched-capacitor circuits. A resulting equivalent filter or signal processor circuit can be implemented by known methods, e.g., in the form of a dedicated circuit on a single chip or as a discrete-component circuit. Implementation of the equivalent circuit as a digital signal processor or a suitably programmed computer is not precluded. While the described techniques are applicable especially to analog or digital electronic signal processing circuits, and are less applicable in the over-all design of recording and playback, storage and retrieval, or transmission and reception systems, the techniques still may be used to advantage in subsystems of such systems. Particularly significant uses of companding filter circuits or signal processors are in portable telephones, radios and TN sets, in hearing aids, computer disk drives, and computer communications networks, for example. Such circuits are especially useful in battery-operated equipment, for reducing noise without undue power dissipation.

Claims: Claims 1. A method for making a linear, continuous-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(t) and corresponding output vector y(t), is input-output equivalent to that prescribed by equations x = Ax + Bu and y = Cx + Du for a state vector x(t) of state variables, and for predetermined matrices A, B, C and D, the method comprising: including processing means in the signal processor for satisfying equations w = Aw + Bu and y = Cw + Du for a derived state vector w(t) = G(t) x(t) of derived state variables, and for matrices A = GG "1 + GAG "1 , B = GB and C = CG '1 , wherein the matrix G(t) has been determined such that the derived state vector w(t) is companded as compared with the state vector x(t) . 2. The method of claim 1, wherein the matrix G has been determined from instantaneous signal values, for instantaneous companding. 3. The method of claim 1, wherein the matrix G has been determined from average signal strength in a time interval, for syllabic companding. 4. The method of claim 1, wherein the matrix G has been determined from input signals. 5. The method of claim l, wherein the matrix G has been determined from output signals. 6. The method of claim l, wherein the matrix G has been determined from internal signals. 7. The method of claim 1, wherein the matrix G has been determined from a combination of signals. 8. The method of claim l, wherein the matrix G has been determined from signals of the signal processor. 9. The method of claim 1, wherein the matrix G has been determined from signals from a further signal processor. 10. The signal processor made by the method of claim 1, 2, 3, 4, 5, 6, 7, 8 or 9. 11. A method for making a linear, discrete-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(n) and corresponding output vector y(n) , is input-output equivalent to that prescribed by equations x(n+l) = Ax(n) + Bu(n) and y(n) = Cx(n) + Du(n) for a state vector x(n) of state variables, and for predetermined matrices A, B, C and D, the method comprising: including processing means in the signal processor for satisfying equations w(n+l) = Aw(n) + Bu(n) and y(n) = Cw(n) + Du(n) for a derived state vector w(n) = G(n) x(n) of derived state variables, and for matrices A = G(n+l)AG _1 (n) , B = G(n+1)B and C = CG" 1 (n) , wherein the matrix G(n) has been determined such that the derived state vector w(n) is companded as compared with the state vector x(n) . 12. The method of claim 11, wherein the matrix G has been determined from instantaneous signal values, for instantaneous companding. 13. The method of claim 11, wherein the matrix G has been determined from average signal strength in a time interval, for syllabic companding. 14. The method of claim 11, wherein the matrix G has been determined from input signals. 15. The method of claim 11, wherein the matrix G has been determined from output signals. 16. The method of claim 11, wherein the matrix G has been determined from internal signals. 17. The method of claim 11, wherein the matrix G has been determined from a combination of signals. 18. The method of claim 11, wherein the matrix G has been determined from signals of the signal processor. 19. The method of claim 11, wherein the matrix G has been determined from signals from a further signal processor. 20. The signal processor made by the method of claim 11, 12, 13, 14, 15, 16, 17, 18 or 19. 21. A computer method for determining specifications of a linear, continuous-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(t) and corresponding output vector y(t) , is input-output equivalent to that prescribed by equations x = Ax + Bu and y = Cx + Du for a state vector x(t) of state variables, and for predetermined matrices A, B, C and D, the method comprising: determining matrices A = GG '1 + GAG "1 , B = GB and C = CG "1 , wherein the matrix G(t) has been determined such that a derived state vector w(t) = G(t) x(t) in equations w = Aw + Bu and y = Cw + Du is companded as compared with the state vector x(t) . 22. A computer method for determining specifications of a linear, discrete-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(n) and corresponding output vector y(n) , is input-output equivalent to that prescribed by equations x(n+l) = Ax(n) + Bu(n) and y(n) = Cx(n) + Du(n) - lS - for a state vector x(n) of state variables, and for predetermined matrices A, B, C and D, the method comprising: determining matrices A = G(n+l)AG- 1 (n) , B = G(n+1)B and C = CG "1 (n) , wherein the matrix G(n) has been determined such that a derived state vector w(n) = G(n) x(n) in equations w(n+l) = Aw(n) + Bu(n) and y(n) = Cw(n) + Du(n) is companded as compared with the state vector x(n) . 23. A system for determining specifications of a linear, continuous-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(t) and corresponding output vector y(t) , is input-output equivalent to that prescribed by equations x = Ax + Bu and y = Cx + Du for a state vector x(t) of state variables, and for predetermined matrices A, B, C and D, the system comprising: means for determining matrices A = GG "1 + GAG "1 , B = GB and C = CG" 1 , wherein the matrix G(t) has been determined such that a derived state vector w(t) = G(t) x(t) in equations w = Aw + Bu and y = Cw + Du is companded as compared with the state vector x(t) . 24. A system for determining specifications of a linear, discrete-time electrical signal processor which has a signal input means for a time-varying signal input vector and a signal output means for a time-varying signal output vector, and which, with respect to any input vector u(n) and corresponding output vector y(n), is input- output equivalent to that prescribed by equations x(n+l) = Ax(n) + Bu(n) and y(n) = Cx(n) + Du(n) for a state vector x(n) of state variables, and for predetermined matrices A, B, C and D, the system comprising: means for determining matrices A = G(n+l)AG- 1 (n) , B = G(n+1)B and C = CG" 1 (n) , wherein the matrix G(n) has been determined such that a derived state vector w(n) = G(n) x(n) in equations w(n+l) = Aw(n) + Bu(n) and y(n) = Cw(n) + Du(n) is companded as compared with the state vector x(n) .

Inventors: TSIVIDIS YANNIS, TSIVIDIS, YANNIS
Applicants: UNIV COLUMBIA, THE TRUSTEES OF COLUMBIA UNIVERSITY
Application year: 1996
Main classification: G06F17
IPC codes: G06F17, G10L21, H03H19, H04B1, H04B3