Matlab for Parabolic Peak Interpolation

Section §G.2 lists Matlab/Octave code for finding quadratically interpolated peaks in the magnitude spectrum as discussed above. At the heart is the qint function, which contains the following:

function [p,y,a] = qint(ym1,y0,yp1)
%QINT - quadratic interpolation of three adjacent samples
%
% [p,y,a] = qint(ym1,y0,yp1)
%
% returns the extremum location p, height y, and half-curvature a
% of a parabolic fit through three points.
% Parabola is given by y(x) = a*(x-p)^2+b,
% where y(-1)=ym1, y(0)=y0, y(1)=yp1.

p = (yp1 - ym1)/(2*(2*y0 - yp1 - ym1));
y = y0 - 0.25*(ym1-yp1)*p;
a = 0.5*(ym1 - 2*y0 + yp1);

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.