Filters of this type are nicely viewed in a *Bode plot* which
shows the magnitude frequency response (in dB) versus a log frequency
axis. In matlab we can say, for example,

sys = tf(1,[1,sqrt(2),1]); bode(sys);to see the frequency response of our normalized second-order Butterworth lowpass filter.

Note that our lowpass is easily converted to a bandpass or highpass filter by changing the transfer-function numerator from to or , respectively:

bode(tf([0 0 1],[1,sqrt(2),1])); % lowpass bode(tf([0 1 0],[1,sqrt(2),1])); % bandpass bode(tf([1 0 0],[1,sqrt(2),1])); % highpass bode(tf([1 0 1],[1,sqrt(2),1])); % notchThese frequency responses are shown in Fig.1.

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