New complex-arithmetic heterodyne filter

Complex arithmetic allows the separation of poles and zeros in the top half of the z-plane from the poles and zeros in the bottom half of the z-plane. Heterodyne techniques can then be used to move the poles and zeros in the top half of the plane counter-clockwise and the poles and zeros in the bottom half of the z-plane clockwise thus maintaining complex-conjugate poles and zeros and hence real-coefficient transfer functions. Using this approach, narrow-band, band-pass and notch filters can be tuned very efficiently. These filters can be easily designed in Matlab using inverse Chebyshev (cheby2) or elliptical (ellip) design techniques. For odd order band-pass filters or for Butterworth or Chebyshev band-pass filters, we need to rotate only the poles and complex zeros, leaving the real zeros in place.