okay, so here's what I came up with...
For the original tabread4~, the impulse response and its Fourier Transform:
g(t)= I-2,2*(-1/6*|t|^3 - 2*t^2 - 11/6*|t| + 1) + I-1,1*(2/3*|t|^3 - 2*t^2 + 4/3*|t|)
G(w)= (1/w^2)*(1/3*cos(2w) - 4/3*cos(w) + 1) + (1/w^4)*(2*cos(2w) - 8*cos(w) + 6)
and for the most recent version of tabread4c~
h(t)= I-2,2*(-1/2*|t|^3 + 5/2*t^2 - 4*|t| + 2) + I-1,1*( 2*|t|^3 - 5*t^2 + 4*|t| - 1)
H(w)= (1/w^3)*(2*sin(2*w) - 4*sin(w)) + (1/w^4)*(18 - 24*cos(w) + 6*cos(2*w))
The graphs shown indicate that tabread4c~ has a faster frequency rolloff (at a maximum rate corresponding to the 1/w^3 term). The frequency response for tabread4~ is shown in red, and tabread4c~ is shown in blue.
The y-axis is dB attenuation, and the x axis is a logarithmic scale for frequency. 0 corresponds to the location of the Nyquist frequency, and each increment corresponds to an octave.
The plot was generated with Octave, and the code is below:
f=pi/16:pi/1024:32*pi; g=1./f.^2.*(1/3*cos(2*f)-4/3*cos(f) + 1) + 1./f.^4.*(2*cos(2*f) - 8*cos(f)+6); h=1./f.^3.*(2*sin(2*f)-4*sin(f)) + 1./f.^4.*(18-24*cos(f)+6*cos(2*f)); plot(log(f/pi)/log(2), 20*log(g+0.00001)/log(10)) hold on plot(log(f/pi)/log(2), 20*log(h+0.00001)/log(10),'b')
