The solution depends on the required frequency range. For a small frequency band, an integrator performs the requested 90° phase shift, for wide band, this would be a complex filter. It's designated Hilbert transform filter in digital signal processing. It's generally easier to generate a 90° phase difference between two signals (relative phase shift) for wide band than an absolute 90° shift. The first can be done by allpass chains and is used e. g. for signal sideband modulation (frequency shift) of audio signals.