Discrete state-space filter and method for processing asynchronously sampled data

A method of processing asynchronously sampled data, comprising:

• a) mapping the coefficients of a linear frequency-domain transfer function H(s) that describes the s-domain representation of an infinite impulse response (IIR) filter or a linear control plant into a continuous-time state-space representation including a state transition matrix A, an input gain matrix B, an output gain matrix C and a input-to-output gain matrix D;
• b) receiving an amplitude uk and time measurement Δtk of a kth data sample;
• c) updating a discrete state transition matrix Φk=eA*Δtk using a first order approximation of the matrix exponential eA*Δtk and a discrete input matrix Γk=(Φk−I)*A−1*B where I is the identity matrix;
• d) updating a discrete state vector Xk=Φk*Xk-1+Γk*uk;
• e) calculating an output amplitude yk=C*Xk+D*uk;
• and
• f) repeating steps b through e for the next k+1 asynchronous data sample.

A method of using a discrete state-space representation of a linear transfer function including a discrete state transition matrix Φ and a discrete input matrix Γ to update a discrete state vector Xk and calculate a output sample yk where Φk defines the extent the previous discrete state vector will affect the current state vector and Γk defines the extent the previous filter state is expected to change due to input data sample, comprising for each kth input data sample uk having a time measurement Δtk:

• updating by a coefficient arithmetic unit (CAU) the discrete state transition matrix Φk=eA*Δtk using a first order approximation of the matrix exponential eA*Δtk where A is a state transition matrix of the continuous-time state-space representation of the linear transfer function;
• updating by the CAU the discrete input matrix Γk=(Φk−I)*A−1*B where I is the identity matrix and B is the input gain matrix of the continuous-time state-space representation of the linear transfer function;
• and
• updating by a filter core the discrete state vector Xk=Φk*Xk-1+Γk*uk.

A discrete time filter for processing asynchronously sampled data, comprising:

• a coefficient arithmetic unit (CAU) configured to receive a portion of a continuous-time state-space representation of a linear frequency-domain transfer function H(s) and a time measurement Δtk of each successive data sample and to update a discrete state transition matrix Φk and a discrete input matrix Γk from the continuous state-space representation and the time measurement of the data sample, said discrete state transition matrix defining the extent the previous discrete state vector Xk-1 will affect the current state vector Xk and said discrete input matrix defining the extent the previous state is expected to change due to input data sample;
• and
• a filter core that stores filter states sample-time independently in a discrete state vector Xk, said core configured to receive the updated discrete state transition matrix Φk and the discrete input matrix Γk from the CAU, an amplitude uk of the data sample and another portion of the continuous-time state-space representation, to update the discrete state vector Xk by propagating the filter states in the previous state vector Xk-1 with the time measurements within the discrete state transition matrix Φk and summing with the sample amplitude uk weighted by the discrete input matrix Γk, and to calculate an output data sample amplitude yk as a function of the updated discrete state vector Xk, the sample amplitude uk and the another portion of the continuous-time state-space representation.