The filter function will only return the same result as ‘y’ (or ‘y1’) for linear-phase FIR filters such as those produced by the fir1 function. For IIR filters, the default design of the bandpass function, you must use the phase-neutral filtfilt function, as I suspect the bandpass function uses by default.
I will let you explore those functions at your leisure.
Your code (with my slight modifications) becomes:
Fs = 10;
t = 1:(1/Fs):200;
s = sin(2*pi*0.1*t) + sin(2*pi*0.5*t);
[y,d] = bandpass(s,[0.06,0.12],Fs);
y2 = filtfilt(d,s);
figure(1)
plot(t, s, t, y2, t, y)
figure(2)
plot(t, y2, '-', t, y, '--')
