Particularly efficient IIR decimators and interpolators can be reached for the sampling rate conversion factor M ( L) = 2. It was observed (Valenzuela & Constantinides, 1983), that a sampling-rate conversion system implemented with two polyphase all-pass branches exhibits favorable pass- stopband characteristics. Actually, the polyphase IIR filter constructed with two all-pass Subfilters is a well-known IIR halfband filter (Ansari, 1983; Valenzuela & Constantinides, 1983; Renfors & Saram ki, 1987; Wegener, 1979; Lutovac, To i?, & Evans 2000; Gazsi, 1985; Sch ssler & Stefen, 1998; Krukowski & Kale, 2003).

The expression for the halfband filter transfer function H ^HB( z) follows from general equations (5.16) and (5.17) for M ( L) = 2,

Hence, an IIR halfband filter consists of two all-pass Subfilters denoted by A ₀ ^HB( z) and A ₁ ^HB( z).

The general magnitude response property for the polyphase IIR filters implemented with all-pass Subfilters is given in (5.24). Consequently, the magnitude response property for a halfband filter is characterized by

When rewriting the above equation in the form

we observe that the magnitude squared function H ^HB( e ^{j ?}) ² is symmetric around ? = ?/2, i.e.,

where ? _p ^HB and ? _s ^HB are passband and stopband edge frequencies, respectively. At the middle of the band, at the frequency ? = ?/2, the squared magnitude...