In filter design, why isn't it possible to have a frequency response with phase 0?
A zero-phase frequency response is real-valued, and, by a property of the Fourier transform, the corresponding impulse response is symmetric. Since it is symmetric (i.e. it is non-zero for $t&lt;0$) it can't be causal, and consequently, it can't be implemented (without adding delay, which defeats the purpose).