A Theoretical Justification for the Asynchronous Application of Linear Prediction to Speech Analysis
Jont B. Allen · The Journal of the Acoustical Society of America · 1974
It is well known that if one has an unknown, causal, linear system h(t) excited by an input signal x(t) and having an output y(t), then minimization of J1 = ∫ −∞∞ [y(t) − ĥ(t)* x(t)]2dt, by variation of ĥ(t), is attained when ĥ(t) equals h(t). Thus, one may determine the unknown system h(t) by this procedure given the system input and output. Not so well known is that h(t) may also be determined, assuming that it is minimum phase and causal, by a minimization with respect to q(t) of the quantity J2 = ∫ −∞∞ [q(t)*y(t))2dt] when the input x(t) is known to be either uncorrelated noise or an impulse, but is otherwise unknown. It will be argued that the above result justified the asynchronous application of linear prediction to speech analysis.