  Electromagnetic wave-based analogue computing has become an interesting
computing paradigm demonstrating the potential for high-throughput, low power,
and parallel operations. In this work, we propose a technique for the
calculation of derivatives of temporal signals by exploiting transmission line
techniques. We consider multiple interconnected waveguides (with some of them
being closed-ended stubs) forming junctions. The transmission coefficient of
the proposed structure is then tailored by controlling the length and number of
stubs at the junction, such that the differentiation operation is applied
directly onto the envelope of an incident signal sinusoidally modulated in the
time domain. The physics behind the proposed structure is explained in detail
and a full theoretical description of this operation is presented,
demonstrating how this technique can be used to calculate higher order or even
fractional temporal derivatives. We envision that these results may enable the
development of further time domain wave-based analogue processors by exploiting
waveguide junctions, opening new opportunities for wave-based single operators
and systems.
