t=linspace(-.5,.5,256);
x=exp(-pi*t.^2*16).*(sin(2*pi*40*t)+0.154*cos(2*pi*47*t)-1.454*cos(2*pi*27*t));
figure;plot(t,x)

tt=linspace(-.5,.5,256*8-7);
xorj=exp(-pi*tt.^2*16).*(sin(2*pi*40*tt)+0.154*cos(2*pi*47*tt)-1.454*cos(2*pi*27*tt));
figure;plot(tt,xorj)

xf=SincInt(x,8,1);
sh=0;
xf=[ xf(1+sh:end) zeros(1,sh)];
figure;plot(tt,xf)
hold on;plot(tt,xorj)
figure;plot(tf,xf-xorj)

function f = SincInt( f,k ,varargin)
% function f = SincInt( f,k ,varargin)
% varargin=1 to keep the beginning and the end the same

nargin=length(varargin);

N=length(f);
f=[zeros(1,N*(k-1)) f];
for  i = 1: N
    f(k*i-k+1:k*i)= [zeros(1,k-1) f(N*(k-1)+i)];
end

f=conv(f,sinc(-60:1/k:60),'same');

if(nargin==1 && varargin{1})
    f=[f(k:length(f)) ];
end

end