repfreq
=======

frequency response



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [ [frq,] repf]=repfreq(sys,fmin,fmax [,step])
    [ [frq,] repf]=repfreq(sys [,frq])
    [ frq,repf,splitf]=repfreq(sys,fmin,fmax [,step])
    [ frq,repf,splitf]=repfreq(sys [,frq])




Arguments
~~~~~~~~~

:sys `syslin` list : SIMO linear system
: :fmin,fmax two real numbers (lower and upper frequency bounds)
: :frq real vector of frequencies (Hz)
: :step logarithmic discretization step
: :splitf vector of indexes of critical frequencies.
: :repf vector of the complex frequency response
:



Description
~~~~~~~~~~~

`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.



Examples
~~~~~~~~


::

    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




See Also
~~~~~~~~


+ `bode`_ Bode plot
+ `freq`_ frequency response
+ `calfrq`_ frequency response discretization
+ `horner`_ polynomial/rational evaluation
+ `nyquist`_ nyquist plot
+ `dbphi`_ frequency response to phase and magnitude representation


.. _freq: freq.html
.. _bode: bode.html
.. _nyquist: nyquist.html
.. _horner: horner.html
.. _calfrq: calfrq.html
.. _dbphi: dbphi.html