# 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.

## Miscellaneous¶

 nrmse(actual, target, **kwargs) Returns RMSE(actual, target) / RMS(target). shift(signal[, amount, value]) Shift the signal amount steps, prepending with value.