But, if I plot the Bode plot of this transfer function I see that it
behaves as a lead compensator, which could have the problem of
amplifying noise at high frequencies.
A single pole at high frequencies is basically a 1st order low pass filter so, beyond a certain frequency noise doesn't get amplified any more. You don't obtain noise attenuation - the ...
A fractional frequency divider is rarely used by itself to provide a divided-down output. Although the divider you describe would on average produce an f0/2.5 signal, such a signal is rarely useful due to the large amount of jitter it has on it, as edges on the output signal obviously have to align with input signal edges.
Instead, a fractional divider is ...
Use a passive resistor network:
Insert a high speed buffer amp to the input if you cannot accept the loading or offset voltage leakage to the input. The buffer cannot be an opamp if you aim it to work perfectly in higher frequency than few kHz.