Represents the system as the transfer function $H(z)=\sum_{i=0}^N b[N-i] z^i / \sum_{j=0}^M a[M-j] z^j$
, where $b$
are elements of the numerator :None:None:`num`, $a$
are elements of the denominator :None:None:`den`, and N == len(b) - 1
, M == len(a) - 1
. Discrete-time TransferFunction
systems inherit additional functionality from the dlti
class.
Changing the value of properties that are not part of the TransferFunction
system representation (such as the :None:None:`A`, :None:None:`B`, :None:None:`C`, :None:None:`D` state-space matrices) is very inefficient and may lead to numerical inaccuracies.
If (numerator, denominator) is passed in for *system
, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g., z^2 + 3z + 5
would be represented as [1, 3, 5]
).
The TransferFunction
class can be instantiated with 1 or 2 arguments. The following gives the number of input arguments and their interpretation:
1:
dltisystem: (StateSpace,TransferFunctionorZerosPolesGain)2: array_like: (numerator, denominator)
Sampling time [s] of the discrete-time systems. Defaults to :None:None:`True` (unspecified sampling time). Must be specified as a keyword argument, for example, dt=0.1
.
Discrete-time Linear Time Invariant system in transfer function form.
Construct the transfer function $H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}$ with a sampling time of 0.5 seconds:
>>> from scipy import signal
>>> num = [1, 3, 3]This example is valid syntax, but raise an exception at execution
... den = [1, 2, 1]
>>> signal.TransferFunction(num, den, 0.5) TransferFunctionDiscrete( array([ 1., 3., 3.]), array([ 1., 2., 1.]), dt: 0.5 )See :
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