Abstract: The magnitude response of unconstrained Chebyshev infinite impulse response (IIR) digital filters usually demonstrates an obvious overshoot in the transition band and large group-delay error near the passband edge. This paper presents a sequential constrained Chebyshev (SCC) method that formulates the design as a series of constrained Chebyshev problems by minimizing the Chebyshev norm of the error between the transition-band frequency response (FR) and a preset monotonically increasing/decreasing transient function subject to a constraint that the maximum magnitude of the passband and stopband FR error is smaller than a given value ρ, the minimum value of which is obtained by a shrinking followed by bisection search. The SCC method can not only render as small as possible the maximum magnitude of the passband and stopband FR error, but also reduce obviously the magnitude overshoot on the transition band and the group-delay error near the passband edge. Simulation results demonstrate the effectiveness of the proposed method.

Key words: IIR filters, Chebyshev design, magnitude overshoot, group-delay error, sequential constrained Chebyshev method