If an ideal bandpass filter has a passband from ωco1 to ωco2, as depicted in Fig. 12-8(b)...

If an ideal bandpass filter has a passband from ωco1 to ωco2, as depicted in Fig. 12-8(b) on p. 353, show that its impulse response can be represented as the convolution of the impulse responses of an ideal highpass filter and an ideal lowpass filter as in

where ωco1 and ωco2 are the bandpass cutoff frequencies. What is the frequency-domain representation of (12.77)?