### XE31CZS Exercise - Signal Modelling and Basic Signal Characteristics

Tasks to do:

• Deterministic signals and their characteristics
• Generate periodical harmonic signal with following parameters:
- amplitude A = 1 , f = 500 Hz , zero phase shift
- sampling parameters: fs = 8000 Hz , to = 0.2 s (duration time).
• Measure basic parameters of generated signal:
a) mean value,
b) variance,
c) power.
• Observe signal samples of generated signals.
• Generate sinusoidal with different frequency and sampling frequency and compare the results
a) fs = 8000 Hz , f = 1100 Hz
a) fs = 8000 Hz , f = 2000 Hz
a) fs = 1000 Hz , f = 250 Hz

• Stochastic signals and their characteristics
• Generate white noise with following distribution:
a) uniform distribution (fcn rand),
b) Gaussian (normal) distribution (fcn randn).
• Observe statistical distribution of signal samples of generated signals (fcn hist).
• Measure basic parameters of generated signals:
a) mean value,
b) variance,
c) power.
• Observe and identify above measured values in sample histograms
• Generate white noise with following parameters:
a) uniform distribution, mean value = 0, variance = 0.1,
b) Gaussian distribution, mean value = 0.5, variance = 0.4.
• Observe distiribution of the sum of 2 or more (5, 10, 20) realizations of random signals with:
a) uniform distribution
b) Gaussian distribution

• Modeling mixed deterministic and stochastic signal
• Generate sinusoidal with following parameters:
- amplitude A = 1 , f = 500 Hz , zero phase shift
- sampling parameters: fs = 8000 Hz , to = 0.2 s (duration time).
• Generate Gaussian white noise with parameters:
- mean value = 0, variance = 0.4.
- fs = 8000 Hz , to = 0.2 s (duration time).
• Add sinusoidal and noise and evaluate SNR (Signal-to-Noise Ration)
• Create mixtures with different SNR from above generated 2 signals (SNR = -5, 0, 5, 10, 20)