convolve_pwc

Graph.convolve_pwc(pwc, kernel)

Create the convolution of a piecewise-constant function with a kernel.

Parameters

• pwc (Pwc) – The piecewise-constant function $\alpha(t)$ to convolve. You can provide a batch of functions, in which case the convolution is applied to each element of the batch.
• kernel (ConvolutionKernel) – The node representing the kernel $K(t)$.

Returns

The sampleable function representing the signal $(\alpha * K)(t)$ (or batch of signals, if you provide a batch of functions).

Return type

Stf

SEE ALSO

Graph.discretize_stf : Discretize an Stf into a Pwc.

Graph.filter_and_resample_pwc : Filter a Pwc with a sinc filter and resample it.

Graph.gaussian_convolution_kernel : Create a convolution kernel representing a normalized Gaussian.

Graph.pwc : Create piecewise-constant functions.

Graph.sample_stf : Sample an Stf at given times.

Graph.sinc_convolution_kernel : Create a convolution kernel representing the sinc function.

Notes

The convolution is

Convolution in the time domain is equivalent to multiplication in the frequency domain, so this function can be viewed as applying a linear time-invariant filter (specified via its time domain kernel $K(t)$) to $\alpha(t)$.

For more information on Stf nodes see the Working with time-dependent functions in Boulder Opal topic.

Examples

Filter a piecewise-constant signal using a Gaussian convolution kernel.

>>> gaussian_kernel = graph.gaussian_convolution_kernel(std=1.0, offset=3.0)
>>> gaussian_kernel
<ConvolutionKernel: operation_name="gaussian_convolution_kernel">
>>> pwc_signal
<Pwc: name="alpha", operation_name="pwc_signal", value_shape=(), batch_shape=()>
>>> filtered_signal = graph.convolve_pwc(pwc=pwc_signal, kernel=gaussian_kernel)
>>> filtered_signal
<Stf: operation_name="convolve_pwc", value_shape=(), batch_shape=()>

Refer to the How to add smoothing and band-limits to optimized controls user guide to find the example in context.