0.5 Speak and sing - pitch correction with psola

Introduction

Pitch correction of the human voice is a common activity, with applications in music, entertainment, and law. It can be used to alter pitch to produce a more accurate or more pleasing tone in music, as well as add distortion effects. Several programs for entertainment use a form of pitch correction to modulate and distort a user's voice, allowing one to sound like a different gender or emulate a celebrity or other well-known voice. Voice distortion is also often required to protect the anonymity of individuals in the criminal justice system. However, it is the first of these applications that we are most interested in - producing a pleasing, tone-accurate song from a human voice.

Implementation

The pitch correction method involves the following basic steps:

• Detection of original pitch
• Parsing of desired pitch frequencies
• Correction of pitch

Pitch detection

First, the pitch of the original signal is determined. This is done using the FAST-Autocorrelation algorithm. This algorithm makes use of the fact that for a signal to have pitch, it must have a somewhat periodic nature, even if it is not a strictly periodic wave. The signal is divided into several small windows, each only a few milliseconds long and containing thousands of samples - enough to detect at least two periods and thus to determine the window's frequency.

Finding periods

R(τ) = f(-τ) * f(τ)

For discrete, finite-length signals, it can be found as a sum of the product of the signal and its offset, in this form:

R(s) = Sum(x(n)x(n-s))

This autocorrelation acts as a match filter: the signal and its offset form will be the most alike when offset s is equal to one period. Thus, the autocorrelation function is at a minimum when the offset corresponds to the length of one period, in samples.

Making it fast

1. The frequency of a window should be relatively close to that of the window before it
2. The first minimum corresponds to the period, so no further minima are needed

By starting at an offset relatively close to the previously found period length (perhaps 20 samples before where the period was found), we can eliminate a few hundred calculations per window. If a minimum is not found in this area, we simply broaden our range and try again. To reduce the computation time further, we also calculate the derivative dR(s)/ds to determine where the minimum occurs. Once we find the first minimum, we are finished with obtaining the frequency for this window, having shaved off up to 70% of our computation time.