IS PHASE IMPORTANT IN SPEECH RECOGNITION?
An FIR filter composed of all zeros that are inside the unit circle is
minimum phase. There are many realizations of a system with a given
magnitude response; one is a minimum phase realization, one is a
maximum-phase realization, others are in-between. Any non-minimum
phase pole-zero system can be decomposed into:
It can be shown that of all the possible realizations of |H(f)|,
the minimum-phase version is the most compact in time. Define:
Then, Emin(n) >= E(n) for all n and all possible realizations
of |H(f)|.
Why is minimum phase such an important concept in speech processing?
We prefer systems that are invertible:
H(z) H-1(z) = 1
We would like both systems to be stable. The inverse of a non-minimum
phase system is not stable.
We end with a very simple question: is phase important in speech
recognition?