87.1 Digital Filter Specifications For example, the magnitude response G(elo) of a digital lowpass filter may be given as indicated below (e Passband. Stopband-*
§7.1 Digital Filter Specifications • For example, the magnitude response |G(ejω)| of a digital lowpass filter may be given as indicated below
87.1 Digital Filter Specifications A S indicated in the iigure, In the passband, defined by0≤0≤0pwe require that G(ej@)=1 with an error +8 1.e 1-8≤Ge)s1+S,|o≤0 In the stopband, defined by≤0≤π,we require that G(ejo)=o with an error 8 i.e., G(ej@)s 8n, @ s slosh
§7.1 Digital Filter Specifications • As indicated in the figure, in the passband, defined by 0≤ω≤ωp , we require that |G(ejω)|≅1 with an error ±δp , i.e., 1- δp ≤ |G(ejω)| ≤ 1+ δp , | ω| ≤ ωp • In the stopband, defined by ωs ≤ω≤π, we require that |G(ejω)|≅0 with an error δs i.e., |G(ejω)| ≤ δp , ωs ≤|ω|≤π
87.1 Digital Filter Specifications passband edge frequency O- stopband edge frequency p-peak ripple value in the passband 8- peak ripple value in the stopband Since g(elo) is a periodic function of a, and G(eo)l of a real-coefficient digital filter is an even function of o As a result, filter specifications are given only for the frequency range 0 sasn
§7.1 Digital Filter Specifications • ωp - passband edge frequency • ωs - stopband edge frequency • δp - peak ripple value in the passband • δs - peak ripple value in the stopband • Since G(ejω) is a periodic function of ω, and |G(ejω)| of a real-coefficient digital filter is an even function of ω • As a result, filter specifications are given only for the frequency range 0 ≤|ω|≤π
87.1 Digital Filter Specifications Specifications are often given in terms of loss function G(o)=-20logoIG(ejo)lin d B Peak passband ripple O1=2090(1-8n)dB Minimum stopband attenuation 03=-20log0(、)dB
§7.1 Digital Filter Specifications • Specifications are often given in terms of loss function G(ω)=-20log10 |G(ejω)| in dB • Peak passband ripple αp= -20log10 (1- δp ) dB • Minimum stopband attenuation αs= -20log10 (δs ) dB
87.1 Digital Filter Specifications magnitude specifications may alternately be given in a normalized form as indicated below Alejo +ε Stopband- Transiton
§7.1 Digital Filter Specifications • Magnitude specifications may alternately be given in a normalized form as indicated below