Interpolation based on sinc function
I'm still not quite sure I understand what you're trying to achieve, but here's an example I cooked up in scilab.

The input is 33 points of a sine wave:

fs = 100; // 10kHz sampling rate
Tin = 1/fs; // Input sampling period
N = 16;
tin = [-N:N]; // Times of samples
f0 = 5;

x = sin(2*%pi*f0/fs*tin + 1.123791823)

clf
subplot(211)
plot(tin,x)


The sampling frequency is 100Hz, the frequency of the sine wave is 5 Hz.

Then, I try to interpolate this up to a sampling frequency of 700Hz using the sinc formula:

Tout = 1/700;
tout = -N:Tout:N;
y = zeros(1,length(tout))
for n = 1:length(tin)
    y =  y + x(n)*sinc(%pi*(tout-tin(n)))
end

plot(tout,y,'r:')
title('Input (blue line) and interpolated (red dotted line)')

subplot(212)
dx = splin(tin,x);
x_interp = interp(tout,tin,x,dx);
plot(tout,y-x_interp)
title('Error')


The results are as plotted below.