frequency response
repf = repfreq(sys) repf = repfreq(sys, frq) repf = repfreq(sys, fmin, fmax) repf = repfreq(sys, fmin, fmax, step) [frq, repf] = repfreq(..) [frq, repf, splitf] = repfreq(..)
A siso or simo linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.
two real numbers (lower and upper frequency bounds)
real vector of frequencies (Hz)
logarithmic discretization step
vector of indexes of critical frequencies.
vector of the complex frequency response
repfreq returns the frequency response calculation of a linear
system. If sys(s) is the transfer function of Sys, repf(k)
equals sys(s) evaluated at s= %i*frq(k)*2*%pi for continuous time systems and
at exp(2*%i*%pi*dt*frq(k)) for discrete time systems (dt is the sampling period).
db(k) is the magnitude of repf(k) expressed in dB i.e.
db(k)=20*log10(abs(repf(k))) and phi(k) is the phase
of repf(k) expressed in degrees.
If fmin,fmax,step are input parameters, the response is calculated
for the vector of frequencies frq given by:
frq=[10.^((log10(fmin)):step:(log10(fmax))) fmax];
If step is not given, the output parameter frq is calculated by frq=calfrq(sys,fmin,fmax).
Vector frq is split into regular parts with the split vector.
frq(splitf(k):splitf(k+1)-1) has no critical frequency.
sys has a pole in the range [frq(splitf(k)),frq(splitf(k)+1)] and
no poles outside.
A=diag([-1,-2]);B=[1;1];C=[1,1]; Sys=syslin('c',A,B,C); frq=0:0.02:5;w=frq*2*%pi; //frq=frequencies in Hz ;w=frequencies in rad/sec; [frq1,rep] =repfreq(Sys,frq); [db,phi]=dbphi(rep); Systf=ss2tf(Sys) //Transfer function of Sys x=horner(Systf,w(2)*sqrt(-1)) // x is Systf(s) evaluated at s = i w(2) rep=20*log(abs(x))/log(10) //magnitude of x in dB db(2) // same as rep ang=atan(imag(x),real(x)); //in rad. ang=ang*180/%pi //in degrees phi(2) repf=repfreq(Sys,frq); repf(2)-x |  |  |
| Version | Description |
| 6.0 | handling zpk representation |