Linear time-invariant system modeling apparatus and method of generating a passive model

A linear time-invariant system modeling apparatus, comprising:

• a processing resource arranged to receive, when in use, model data constituting to a model of a linear time-invariant system, the model data including residual value data and scattering data, wherein
• the processing resource is arranged to perform, when in use, a singular value decomposition in respect of the scattering data, the scattering data corresponding, when expressed in matrix form, to a scattering matrix in a state-space representation of the model;
• and
• the processing resource is also arranged to use, when in use, a result of the singular value decomposition in order to generate residual value modification data for a non-passive interval of a predetermined frequency range of a linear time-invariant system, and apply the residual value modification data to the residual value data, the residual value data corresponding, when expressed in the matrix form, to a residual value matrix in the state-space representation of the model,
• wherein the singular value decomposition is performed using the following relationship, when expressed in matrix form:
• S=UΣVH
• where:
• S corresponds to a scattering matrix comprising the scattering data,
• U is a unitary matrix,
• Σ is a positive, real-valued, diagonal matrix, and
• VH is a unitary transformation matrix.

A computer implemented method of generating a passive model of a linear time-invariant system from a non-passive model of the linear time-invariant system, the method comprising:

• receiving, using a processing resource, model data constituting to a model of the linear time-invariant system, the model data including residual value data and scattering data;
• performing, using the processing resource, a singular value decomposition in respect of the scattering data, the scattering data corresponding, when expressed in matrix form, to a scattering matrix in a state-space representation of the model;
• using a result of the singular value decomposition in order to generate, using the processing resource, residual value modification data for a non-passive interval of a predetermined frequency range of a linear time-invariant system;
• applying, using the processing resource, the residual value modification data to the residual value data, the residual value data corresponding, when expressed in matrix form, to a residual value matrix in the state-space representation of the model.