s 87.1 Digital Filter Specifications For example, the magnitude response G(ejo)l of a digital lowpass filter may be given as indicated below 1+8 1-8p Passband. topband Transiton
§7.1 Digital Filter Specifications • For example, the magnitude response |G(e j)| of a digital lowpass filter may be given as indicated below
s 87.1 Digital Filter Specifications &. AS indicated in the figure, in the passband, defined by0≤0≤0p,we require that G(ej@)≤ I with an error±8p, l.e., 1-8psG(eo≤1+8p,|o≤p · In the stopband, defined by a≤≤π,we require that g(ejo)=o with an error 8 ie,G(eo)s8p,0ss|0l≤π
§7.1 Digital Filter Specifications • As indicated in the figure, in the passband, defined by 0p , we require that |G(e j)|1 with an error p , i.e., 1- p |G(e j)| 1+ p , | | p • In the stopband, defined by s , we require that |G(e j)|0 with an error s i.e., |G(e j)| p , s ||
s 87.1 Digital Filter Specifications p- passband edge frequency stopband edge frequency 8p- peak ripple value in the passband °8、- peak ripple value in the stopband Since g(ejo)is a periodic function of o, and G(ejo)l of a real-coefficient digital filter is an even function of o As a result, filter specifications are given only for the frequency range0so≤兀
§7.1 Digital Filter Specifications • p - passband edge frequency • s - stopband edge frequency • p - peak ripple value in the passband • s - peak ripple value in the stopband • Since G(e j) is a periodic function of , and |G(e j)| of a real-coefficient digital filter is an even function of • As a result, filter specifications are given only for the frequency range 0 ||
s 87.1 Digital Filter Specifications Specifications are often given in terms of loss function G(o)=-20log1o G(ejo)l in dB Peak passband ripple ap=-20l0g10(1-8p)dB Minimum stopband attenuation 、=-20log10(85)dB
§7.1 Digital Filter Specifications • Specifications are often given in terms of loss function G()=-20log10 |G(e j)| in dB • Peak passband ripple p = -20log10 (1- p ) dB • Minimum stopband attenuation s = -20log10 (s ) dB
s 87.1 Digital Filter Specifications Magnitude specifications may alternately be given in a normalized form as indicated below Jo 1+e Passband Stopband一 o Transiton band
§7.1 Digital Filter Specifications • Magnitude specifications may alternately be given in a normalized form as indicated below