I know except for some special cases, aliasing is unavoidable. Assume we time-limit a function, $f(t)$, so that it is zero outside an interval say $[0,T]$ to form $y(t)$. Then, in the frequency domain, infinite frequency components are introduced.
If the system that makes this time limitation has impulse response $h(t)$, we have its Fourier representation $H(u)$. We can then calculate $Y(u)$ using convolution to obtain: $$Y(u)=F(u)*H(u)$$ Obviously, it has frequency components that are replicated to infinity. This phenomenon is because of sliding it across the original function to calculate Convolution.
Could anyone possibly let me know in what condition we can have band-limited input and output.