Complex Signals – Quadrature Filters – Interpolators
Maurice Bellanger · Digital Signal Processing · 2024
Complex signals in the form of sets of complex numbers are currently used in digital signal analysis. This chapter examines analytic signals – a particular category of complex signal. Such signals exhibit some interesting properties and occur primarily in modulation and multiplexing. Analytic signals correspond to causal signals in which time and frequency are exchanged. The properties of analytic signals are deduced from the properties of causal signals by exchanging time and frequency. A recursive phase shifter is characterized by the fact that the numerator and denominator of its Z-transfer function are image polynomials. Interpolation consists of calculating signal samples between known samples. In the frequency domain, Lagrange interpolation corresponds to “max-flat” filtering – that is, the derivatives of the frequency response vanish at the origin. A particularly important case is Lagrange interpolation, which corresponds to a max-flat filter, whose frequency response derivatives vanish at the origin.