Abstract
A new design method for maximally flat IIR fullband differentiators with flat group delay responses is derived in this paper. The design method starts from the flatness conditions of magnitude response and group delay response at the origin. After mathematical manipulations it shows that presented design method reduces to solving the system of linear equations. By increasing the orders of polynomials in numerator and denominator, degrees of flatness are increased, that is improvement in magnitude responses and group delay responses in terms of flatness is obtained.
Highlights
Fullband differentiators are needed in various applications [1]-[7] where time-derivative of signal at input port need to be computed
From equation (1) it follows that maximally flat impulse response filters (IIR) fullband differentiators with flat group delay responses are characterized by flatness conditions
The method derived in [24] is extended to design of maximally flat IIR fullband differentiators with flat group delay responses, whose transfer function can be expressed as [25], [16]
Summary
Fullband differentiators are needed in various applications [1]-[7] where time-derivative of signal at input port need to be computed Those filters, as any other type of filter functions, can be designed as finite impulse response filters (FIR) [8]-[15] and infinite impulse response filters (IIR) [16]-[23]. The method derived in [24] is extended to design of maximally flat IIR fullband differentiators with flat group delay responses, whose transfer function can be expressed as [25], [16]. H(ejω) = |H(ejω)|ejθ(ω) at ω = 0, and using previous equations, it shows that maximally flat IIR fullband differenztiators with flat group delay responses have frequency responses satisfying.
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