# 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 $$\alpha(t)$$.