Making a Bandpass Filter from a Lowpass Filter

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Making a Bandpass Filter from a Lowpass Filter

**Figure 9.13:** Construction of a bandpass filter using demodulation, lowpass filtering, and remodulation.
$\begin{figure}\input fig/BPF.pstex_t \end{figure}$

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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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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Spectral Audio Signal Processing
    The Filter Bank Summation (FBS) Interpretation of the Short Time Fourier Transform (STFT)
       The DFT Filter Bank
          Making a Bandpass Filter from a Lowpass Filter