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    %% Numeric Values of Frequency-Domain Characteristics of SISO Model  
% This example shows how to obtain numeric values of several frequency-domain
% characteristics of a SISO dynamic system model, including the peak gain,
% dc gain, system bandwidth, and the frequencies at which the system gain
% crosses a specified frequency.   

%% 
% Create a transfer function model and plot its frequency response. 
H = tf([10,21],[1,1.4,26]); 
bodeplot(H)    

%%
% Plotting the frequency response gives a rough idea of the frequency-domain
% characteristics of the system. |H| includes a pronounced resonant peak,
% and rolls off at 20 dB/decade at high frequency. It is often desirable
% to obtain specific numeric values for such characteristics.  

%% 
% Calculate the peak gain and the frequency of the resonance. 
[gpeak,fpeak] = getPeakGain(H);
gpeak_dB = mag2db(gpeak) 

%%
% |getPeakGain| returns both the peak location |fpeak| and the peak gain
% |gpeak| in absolute units. Using |mag2db| to convert |gpeak| to decibels
% shows that the gain peaks at almost 18 dB.  

%% 
% Find the band within which the system gain exceeds 0 dB, or 1 in absolute
% units. 
wc = getGainCrossover(H,1) 

%%
% |getGainCrossover| returns a vector of frequencies at which the system
% response crosses the specified gain. The resulting |wc| vector shows that
% the system gain exceeds 0 dB between about 1.3 and 12.2 rad/s.  

%% 
% Find the dc gain of |H|. 
%
% The Bode response plot shows that the gain of |H| tends toward a finite
% value as the frequency approaches zero. The |dcgain| command finds this
% value in absolute units. 
k = dcgain(H);  

%% 
% Find the frequency at which the response of |H| rolls off to –10 dB relative
% to its dc value. 
fb = bandwidth(H,-10); 

%%
% |bandwidth| returns the first frequency at which the system response drops
% below the dc gain by the specified value in dB.