Creates a piecewise-constant function by discretizing a sampleable function.
Use this function to create a piecewise-constant approximation to a sampleable
function (obtained, for example, by filtering an initial
piecewise-constant function).
- Parameters
stf (Stf) – The sampleable function \(v(t)\) to discretize. The values of the
function can have any shape. You can also provide a batch of
functions, in which case the discretization is applied to each
element of the batch.
duration (float) – The duration \(\tau\) over which discretization should be
performed. The resulting piecewise-constant function has this
duration.
segment_count (int) – The number of segments \(N\) in the resulting piecewise-constant
function.
sample_count_per_segment (int, optional) – The number of samples \(M\) of the sampleable function to take when
calculating the value of each segment in the discretization. Defaults
to 1.
name (str, optional) – The name of the node.
- Returns
The piecewise-constant function \(w(t)\) obtained by discretizing
the sampleable function (or batch of piecewise-constant functions, if
you provided a batch of sampleable functions).
- Return type
Pwc
Notes
The resulting function \(w(t)\) is piecewise-constant with \(N\)
segments, meaning it has segment values \(\{w_n\}\) such that
\(w(t)=w_n\) for \(t_{n-1}\leq t\leq t_n\), where \(t_n= n \tau/N\).
Each segment value \(w_n\) is the average of samples of \(v(t)\)
at the midpoints of \(M\) equally sized subsegments between
\(t_{n-1}\) and \(t_n\):
\[w_n = \frac{1}{M}
\sum_{m=1}^M v\left(t_{n-1} + \left(m-\tfrac{1}{2}\right) \frac{\tau}{MN} \right).\]