Returns

-------

H : TimeResponseData

Markov parameters / impulse response [D CB CAB ...] represented as

a :class:`TimeResponseData` object containing the following properties:

* time (array): Time values of the output.

* outputs (array): Response of the system. If the system is SISO,

the array is 1D (indexed by time). If the

system is not SISO, the array is 3D (indexed

by the output, trace, and time).

* inputs (array): Inputs of the system. If the system is SISO,

the array is 1D (indexed by time). If the

system is not SISO, the array is 3D (indexed

by the output, trace, and time).

H : ndarray

First m Markov parameters, [D CB CAB ...]

Notes

-----

H = H.reshape(q,m,p) # output, time*input -> output, time, input

H = H.transpose(0,2,1) # output, input, time

# Create unit area impulse inputs

inputs = np.zeros((p,p,m))

trace_labels, trace_types = [], []

for i in range(p):

inputs[i,i,0] = 1/dt # unit area impulse

trace_labels.append(f"From {data.input_labels[i]}")

trace_types.append('impulse')

if q == 1 and p == 1:

H = np.squeeze(H)

# Markov parameters as TimeResponseData with unit area impulse inputs

# Return the first m Markov parameters

return TimeResponseData(time=data.time[:m],

outputs=H,

output_labels=data.output_labels,

inputs=inputs,

input_labels=data.input_labels,

trace_labels=trace_labels,

trace_types=trace_types,

transpose=data.transpose,

plot_inputs=False,

issiso=data.issiso)

return H if not data.transpose else np.transpose(H)