Phase as Timing

Cutoff Phase Is a Named Model Point

At cutoff the ideal first-order model uses a checked named phase point. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The low-pass cutoff point has a checked lag

At normalized index 1, the low-pass squared ratio is 1/2 and the phase magnitude is 1/8 cycle.

x=1,∣H∣2=12,ϕ=18x=1,\quad |H|^2={1\over 2},\quad \phi={1\over 8}
Low-pass cutoff phaseKind, ratio, lag, and phase bar are checked.ratiophaselagphase

The high-pass cutoff point has a checked lead

The high-pass point keeps the same 1/2 squared ratio but the direction is lead.

x=1,∣H∣2=12,ϕ=18x=1,\quad |H|^2={1\over 2},\quad \phi={1\over 8}
High-pass cutoff phaseThe checked direction is lead, not lag.ratiophaseleadphase