Signal (nengolib.signal)¶
Linear Systems¶
LinearSystem(sys[, analog]) |
Generic linear system representation. |
cont2discrete(sys, dt[, method, alpha]) |
Convert linear system from continuous to discrete time-domain. |
discrete2cont(sys, dt[, method, alpha]) |
Convert linear system from discrete to continuous time-domain. |
Model Reduction¶
pole_zero_cancel(sys[, tol]) |
Pole/zero cancellation within a given tolerance. |
modred(sys, keep_states[, method]) |
Reduces model order by eliminating a subset of states. |
balance(sys) |
Transforms a linear system to its balanced realization. |
balred(sys, order[, method]) |
Reduces a linear system to given order using balance and modred. |
Realizations¶
Identity |
Scaled realization given only by the radii. |
Balanced |
Balanced realization given by the Gramiam matrices. |
Hankel |
Scaled realization given by the Hankel singular values. |
L1Norm([rtol, max_length]) |
Scaled realization given by the L1-norm of the system’s state. |
H2Norm |
Scaled realization given by the H2-norm of the system’s state. |
Distributions¶
EvalPoints(sys, process[, n_steps, dt]) |
Samples the output of a LinearSystem given some input process. |
Encoders(sys, process[, n_steps, dt]) |
Samples axis-aligned encoders from the maximum radii of a LinearSystem. |
Learning¶
pes_learning_rate(epsilon, activities, t[, dt]) |
Determine the ideal learning rate for PES without noise or filtering. |
Lyapunov Theory¶
l1_norm(sys[, rtol, max_length]) |
Computes the L1-norm of a linear system within a relative tolerance. |
state_norm(sys[, norm]) |
Computes the norm of each dimension of x in the state-space. |
control_gram(sys) |
Computes the controllability/reachability gramiam of a linear system. |
observe_gram(sys) |
Computes the observability gramiam of a linear system. |
hsvd(sys) |
Compute Hankel singular values of a linear system. |
balanced_transformation(sys) |
Computes the balancing transformation, its inverse, and eigenvalues. |
