AE2M99CZS exercise - Discrete-time systems, difference equation, transfer function.
Tasks to do:
Checked result - WRITTEN TEST (6
points) General properties of Z-transform and 1st order systems.
ATTENTION! The test cannot be written in any other time! In the
case of apologized absence you will recieve points according to the
same rules as for any other seminar.
Properties of 2nd order systems, inverse Z-transform of
higher-order systems.
For discrete-time systems described by following difference
equations draw block scheme, compute difference equation, transfer
function, zeros and poles of transfer function, impulse
response, and estimate frequency response.
y[n] = x[n] + 0.81 x[n-2]
Observe the change of the frequency response and zero-poles locations
for the following systems:
Only in MATLAB: "all=pole" filter with the pair of complex conjugate poles p_1 = 0.9
*exp ( +/- j * pi/4 )
y[n] = x[n] + x[n-1] + x[n-2] + ... + x[n-9] ;
y[n] = x[n] - x[n-6]
y[n] = x[n] - x[n-9]
For above described system observe in MATLAB:
zeros and poles of transfer function (fnc zplane, roots)
frequency response of the system (fnc freqz)
impulse response of given system (fnc impz)
check also interactive tool fvtool
Realization of filtering in MATLAB
Realize filtering in MATLAB for selected systems using function
filter and observe PSD and spectrograms of filtered
signals. Choose some of the following signals:
- white noise of length 10000
- speech signals (fs = 16 kHz) :
sm2.bin - (Czech utterance "1 0 6 4 7" - male),
(Binary signals can be loaded using function loadbin.m)
When speech signals are filtered, try also illustrative listening
(function sound).