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First-Order Allpass Phase
Estimate the phase shift and group delay of an ideal analog allpass section.
Frequency (Hz): 0–96000; −90° corner frequency (Hz): 0.01–96000
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First-Order Allpass Phase
Frequency (Hz): 1000 −90° corner frequency (Hz): 1000
- Phase shift (°)
- -90.000000
- Group delay (ms)
- 0.159155
For H(s)=(ωc−s)/(ωc+s), ωc=2πfc, magnitude stays 1. Phase φ=−2 atan(f/fc); group delay τ=1/[πfc(1+(f/fc)²)] seconds. Results use degrees and milliseconds. At f=fc, phase is −90°. At DC phase is 0° but group delay remains finite. Group delay is the negative phase derivative, not phase divided by frequency and not a constant time offset. This analog model does not predict a digital plugin’s coefficients, latency, sample-rate warping, acoustic response or cascaded filters. Verify the actual device before alignment.
Methodology
How it works
For H(s)=(ωc−s)/(ωc+s), ωc=2πfc, magnitude stays 1. Phase φ=−2 atan(f/fc); group delay τ=1/[πfc(1+(f/fc)²)] seconds. Results use degrees and milliseconds. At f=fc, phase is −90°. At DC phase is 0° but group delay remains finite. Group delay is the negative phase derivative, not phase divided by frequency and not a constant time offset. This analog model does not predict a digital plugin’s coefficients, latency, sample-rate warping, acoustic response or cascaded filters. Verify the actual device before alignment.
Method and assumptions documented by Techrider.live
2026-11-15
Frequently asked questions
Can I replace this with a fixed delay?
Only approximately over a narrow band. An allpass section changes phase and group delay with frequency while preserving ideal magnitude. A fixed delay has constant group delay.