Making a Bandpass Filter from a Lowpass Filter

Figure 8.13: Construction of a bandpass filter using demodulation, lowpass filtering, and remodulation.

Figure 8.13 shows how a bandpass filter can be made using a lowpass filter together with modulation. The input spectrum is frequency-shifted by $-\omega _c$, lowpass filtered, then frequency-shifted by $+\omega_c$, thereby creating a bandpass filter centered at frequency $\omega_c$. From our experience with rectangular-window transforms (Fig.8.11 being one example), we can say that the bandpass-filter bandwidth is equal to the main-lobe width of the aliased sinc function, or $4\pi/N$ radians per sample (measured from zero-crossing to zero-crossing).