Methods and systems for designing and making signal-processor circuits with internal companding, and the resulting circuits
AssigneeThe Trustees of Columbia University in the City of New York
InventorYannis Tsividis
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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. G(t) may be chosen for instantaneous or syllabic companding of the state vector. A corresponding technique applies to discrete-time circuits.
Claims10
A linear, continuous-time electrical signal processor having input-output characteristics as prescribed for a time varying signal input vector u(t) and a time-varying signal output vector y(t) specified for a state vector x(t) of state variables by equations
- {dot over (x)}=Ax+Bu
- and
- y=Cx+Du
- wherein A, B, C, and D are prescribed matrices,
- having a signal input means for the input vector u(t) and a signal output means for the output vector y(t), and
- being prescribed for a state vector w(t) of state variables by equations
- {dot over (w)}=Âw+{circumflex over (B)}u
- and
- y=Ĉw+Du
- wherein
- Â={dot over (G)}G−1+GAG−1, {circumflex over (B)}=GB
- and
- Ĉ=CG−1
- with G(t) being preselected such that the state vector is w(t) is companded as compared with the state vector x(t).
A linear, discrete-time electrical signal processor having input-output characteristics as prescribed for a time-varying input vector u(n) and a time-varying signal output vector y(n) specified for a state vector x(n) of state variables by equations
- x(n+1)=Ax(n)+Bu(n)
- and
- y(n)=Cx(n)+Du(n)
- wherein A, B, C and D are prescribed matrices,
- having a signal input means for the input vector u(n), and a signal output means for the signal output vector y(n), and
- being prescribed for a state vector w(n) of state variables by equations
- w(n+1)=Âw(n)+{circumflex over (B)}u(n)
- and
- y(n)=Ĉw(n)+Du(n)
- wherein
- Â=G(n+1)AG−1(n), {circumflex over (B)}=G(n+1)B
- and
- Ĉ+CG−1(n)
- with G(n) being preselected such that the state vector w(n) is companded as compared with the state vector x(n).
Dependencies are inferred from the claim text.