Spectral shifts with pseudospectral

[xtalax]

So, a user posted this system, dealing with an integrated shift. This is tough to adequately discretize, but we could do this easily in the frequency domain.

So a shift in the time domain is equal to multiplication by a complex exponential in the frequency domain:

$$v(t - \tau) \rightarrow V(\omega)e^{-j{\omega}{\tau}}$$

Of course, his convolution integral is a simple multiplication in the frequency domain:

$$\int\limits_0^t v(t-x)i(x) dx \rightarrow V(\omega)I(\omega)$$

So this type of system becomes very easy to discretize in the frequency domain.

I think this serves as a motivation for having a robust set of time-frequency domain rewrite rules, leveraging MetaTheory.jl to find analytic "discretizations" where possible