There are two part in this project: signal reconstruction from STFT magnitude spectra and Time-Scale Modification (TSM). In the first part, we implement 3 algorithm: GL, RTISI, and RTISI-LA, followed by comparison of their performance based on SER function mentioned in the paper [3]. In the second part, we employ the RTISI-LA method on Time-Scale Modification, and compare its performance with classic WSOLA method on the given sample data.

Linear predictive coding (LPC) is a widely used technique in audio signal compression. The philosophy of LPC is related to the human voice production. Then vocal fold generate the sound source e(n), which then go through a linear, time-varying filter h(n). The output signal can be represented as: x(n) = e(n) ∗ h(n)

The source signal could be an quasi-periodic pulses (voiced speech) or random noise (unvoiced speech). The filter is modeled as all-pole filter, which can be represented as: If we could extract the coefficients ak, k = 1...p of the all pole filter, then we can reconstruct the signal x(n) by using the current input e(n) and past samples x(n−k), k = 1...p using the following equation

In this report, we implement a Vocoder based on LPC method above, to achieve signal compression and reconstruction. To be more specific, we first cut the signal into small frames and then for each frame, we add a window function and then encoded the windowed signal into a few coefficients based on LPC method. These coefficients include:

1. Pitch
2. Gain
3. Poles coefficients ak, k = 1...p

Then, we try to reconstruct each frame signals based on these coefficients and overlap add them to recover the original signal. Finally, we evaluate the quality of the synthesized signal by ear. There is a trade-off between the compression rate and the quality of the synthesized speech. Our goal is to use the least number of coefficients to reconstruct the original signal with the best quality. After experiment, we found that, for a 16 kHz frame rate speech signal, we only need to store 454 samples per second to resynthesize the original signal in a pretty high standard.