Making a Bandpass Filter from a Lowpass Filter

Figure 9.13: Construction of a bandpass filter using demodulation, lowpass filtering, and remodulation.

Figure 9.13 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.9.11 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).

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Modulation by a Complex Sinusoid