### AE2M99CZS exercise - Discrete-time systems, difference equation, transfer function.

• 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.

1. y[n] = x[n] + 0.81 x[n-2]

2. Observe the change of the frequency response and zero-poles locations for the following systems:
• y[n] = x[n] + 0.81 x[n-2]
• y[n] = x[n] + 0.64 x[n-2]
• y[n] = x[n] + 0.925 x[n-2]
• y[n] = x[n] - 0.81 y[n-2]
• y[n] = x[n] - 0.64 y[n-2]
• y[n] = x[n] - 0.925 y[n-2]

3. y[n] = 0.4455 x[n-1] + 1.2728 y[n-1] - 0.81 y[n-2]

4. Only in MATLAB: "all=pole" filter with the pair of complex conjugate poles p_1 = 0.9 *exp ( +/- j * pi/4 )

5. y[n] = x[n] + x[n-1] + x[n-2] + ... + x[n-9] ;

6. y[n] = x[n] - x[n-6]

7. 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),