convolve_pwc

static OperationNamespace.convolve_pwc(pwc, kernel_integral)

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

Parameters
  • pwc (TensorPwc) – 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_integral (Function) – The node representing the function that computes the integral of 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

Notes

The convolution is

\[(\alpha * K)(t) \equiv \int_{-\infty}^\infty \alpha(\tau) K(t-\tau) d\tau.\]

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 \(\alpha(t)\).