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+6 Passband. Transiton
§7.1 Digital Filter Specifications • For example, the magnitude response |G(ej)| of a digital lowpass filter may be given as indicated below
87.1 Digital Filter Specifications .. As indicated in the figure, in the passband, defined by Usapp'vre require that g(eo)∈1 with an error±8n, 1.e ● 1-8sG(eo)≤1+8p,|o≤op · In the stopband, defined by a≤0≤,we require that G(ejo eo with an error 8 ie,G(e°)≤8,0,so≤π
§7.1 Digital Filter Specifications • As indicated in the figure, in the passband, defined by 0p , we require that |G(ej)|1 with an error p , i.e., 1- p |G(ej)| 1+ p , | | p • In the stopband, defined by s , we require that |G(ej)|0 with an error s i.e., |G(ej)| p , s ||
87.1 Digital Filter Specifications @n- passband edge frequency s- stopband edge frequency 8p- peak ripple value in the passband 8s-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≤π
§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(ej) is a periodic function of , and |G(ej)| of a real-coefficient digital filter is an even function of • As a result, filter specifications are given only for the frequency range 0 ||
=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 20log10(1-8p)dB \. Minimum stopband attenuation a、=-200g10(8、)dB
§7.1 Digital Filter Specifications • Specifications are often given in terms of loss function G()=-20log10 |G(ej)| in dB • Peak passband ripple p= -20log10 (1- p ) dB • Minimum stopband attenuation s= -20log10 (s ) dB
87.1 Digital Filter Specifications Magnitude specifications may alternately be given in a normalized form as indicated below passband Transiton band
§7.1 Digital Filter Specifications • Magnitude specifications may alternately be given in a normalized form as indicated below