Design of subband transmission systems in time and frequency domain
Takuro Kida, Leopoldo Rideki Yoshioka · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1991
Abstract Consider a system in which N time‐invariant linear circuits Hk(ω)(k=1∼N) are connected in parallel and to each of which M parallel time‐invariant linear circuits Hkm(ω)(k=1 ∼N; m=1∼M) are connected in cascade. Then consider that a certain class of band‐limited signals f(t) is impressed on such a system, and the equal‐interval sampled values gkm(nT+akm)(k=1∼N : m=1 ∼M : n=0, ±1, ±2,…; T>0; akm of the output signals gkm(t)(k=1∼N; m=1∼M) are obtained. By multiplying the sampled values by the interpolation function Økm(t)(k=1∼N; m=1 ∼M), which is obtained by the convolution of the time functions Økm(t)(k=1∼N; m=1 ∼M), and by summing up, an approximation formula y(t) is determined. A unified investigation is made on the approximation problem using y(t) for the response g(t) when the original signal f(t) passes through a given filter H(ω). First, the error e(t)=g(t)‐y(t) is considered for given Hk(ω)(k=1∼N), and Hkm(ω)(k=1∼N; m=1∼M) over the set of f(t) belonging to the considered set of waveforms, and a formula is derived which represents the upper bound ∼max(t) of the error in a form where the interpolation functions Økm(t) and Øk(t) are separated. Then, based on the derived formula, an effective design method for the interpolation filter is established, based on the coefficient equation and linear programming, assuming that all of the interpolation filters are constructed as FIR type. Finally, the optimization of the system with a hierarchical structure is discussed.