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The LP filter so far presented attempts to fit an allpole model using
the leastmeansquares distance metric.

The lower formants contain more energy and therefore are preferentially
modeled with respect to the higher formants

A preemphasis filter,
is often used to boost the higher frequencies. Typically , or the optimal preemphasis is used.

If reconstructing the speech the inverse filter should be used:
Speech Vision Robotics group/Tony Robinson