Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

IIR Filters 19-290−10200150Magnitude response (dB)−20−30−40−50−60−70−80−90Phase response (°)100500−50−100−150−1000 0.1 0.2 0.3 0.4 0.5f−2000 0.1 0.2 0.3 0.4 0.5fFIGURE 19.19Frequency response of the HPF designed using bilinear transformation.1/(1 + ε 2 )|H BP ( f )| 21ff s1 f p1 f p2 f s211/(1 + ε 2 )δ 2 |H BS ( f )| 2 f s1δ 2(a)00.5(b)0f p1f s2f p20.5fFIGURE 19.20specification.Magnitude specifications for digital BPF and BSF: (a) digital BPF specification and (b) digital BSFl p1 ¼ 2T tan (pf p1 ) l p2 ¼ 2T tan (pf p2 )l s1 ¼ 2T tan (pf s1 ) l s2 ¼ 2T tan (pf s2 )(19:71)and keeping the same e and d.Now, we need a transformation between an analog BPF and an analog LPF. To distinguish between thevariable s and l for the two filters, let us use s 0 and l 0 for the analog LPF and s and l for the analog BPF,respectively. A transformation for converting an analog LPF to an analog BPF is given by