An LPC vocoder takes a speech waveform sampled at 8kHz and compresses it to a lower bitrate for transmission by modeling the human vocal tract as a linear system over frames of 25ms. It estimates the vocal tract spectrum and pitch in each frame, transmitting this data which is much smaller than sending the raw samples. At decoding, the estimated spectrum is excited with an impulse train of the estimated pitch to reproduce the speech. The document also describes a gain estimation method that utilizes speech waveform envelopes to estimate gains for voiced and unvoiced frames such that the synthetic speech amplitude matches the envelope.

1. LPC (Linear Predictive Coder) Implemented in MATLAB
ABSTRACT
An LPC vocoder (Linear-Predictive Coder), is a lossy compression technique
that is highly optimized for low-bitrate speech transmission. The problem here that we
solve is to take a speech waveform with an 8kHz sampling rate, code it to a much lower
bit-rate so that it can be transmitted over a channel, and finally decode it to a signal that is
of the same quality.
To do this we take advantage of the fact that the human vocal tract can be modelled
as a linear system for a period of about 25 ms. We estimate the spectrum of the vocal
tract in frames of 25 ms (see LPC analysis) and estimate the pitch of the speech once
every 10 ms. We then transmit this data, which is much less than transmitting 8000
samples every second. To reproduce the speech we simply excite the estimated spectrum
with an impulse train of the estimated pitch..
A gain estimation method for an LPC vocoder which utilizes shape indexes. The
gain is estimated based on the envelope of the speech waveform. The gain is estimated
such that the maximum amplitude of the synthetic speech just reaches the speech
waveform envelope. The gain during voiced subframes is estimated as the minimum of
the absolute value of ratio of the envelope and the impulse response of the LPC filter.
The gain during unvoiced subframes is estimated as the minimum of the absolute value of
the ratio of the envelope and the noise response of the LPC filter. The method results in a
fast technique for estimating the gain.