dhofun.m

Normalised damped harmonic oscillator response function in magnetic resonance notation. This is the standard shape of a phonon band: a resonance at the natural frequency of the oscillator, broadened by damping, and vanishing quadratically at zero frequency, which a Lorentzian centred at the same place does not do. In the weak damping limit the function tends to a Lorentzian of the same width. Evaluation uses frequencies scaled by nat_freq to avoid intermediate overflow in single precision. The function is set to zero at non-positive arguments, and at positive arguments it is evaluated as (2*g/(pi*w0))*u^2/((u^2-1)^2+(g*u)^2), where u is the argument divided by the natural frequency w0 and g is the damping rate divided by the natural frequency. The output array inherits the class of the input array.

Syntax

    y=dhofun(x,nat_freq,fwhm)

Parameters

            x - argument values, a real array of any dimension;
                the function is zero at non-positive arguments

     nat_freq - natural frequency of the undamped oscillator, a
                positive real scalar, in the same units as x; the
                maximum of the function sits exactly here

         fwhm - damping rate of the oscillator, a positive real
                scalar, in the same units as x; for this respon-
                se function it is exactly the full width at half-
                maximum, at any damping

Outputs

            y - function values at the points specified in x, an
                array of the same size and type as x, normalised
                to unit integral over positive arguments

See also

gaussfun.m, lorentzfun.m, lorentzcon.m, Kernel utilities

Version 2.13, authors: Ilya Kuprov