Processing math: 100%
We can derive an exact solution of the discrete equations
- We have a linear, homogeneous, difference equation for un.
- Has solutions un∼IAn, where A is unknown (number).
- Here: ue(t)=Icos(ωt)∼Iexp(iωt)=I(eiωΔt)n
- Trick for simplifying the algebra: un=IAn, with A=exp(i˜ωΔt), then find ˜ω
- ˜ω: unknown numerical frequency (easier to calculate than A)
- ω−˜ω is the phase error
- Use the real part as the physical relevant part of a complex expression