Exercises collection

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Exercises Read Carefully These exercises are provided only to give an example of possible exams questions. Any topic object of the lessons can be the object of the written and of the oral exam. 1 Sampling 1.1 Example 1 Your acquisition system is configured as follows:  Sampling rate: 250 Hz  Number of samples: 2500  Antialiasing Filter Cut-off frequency: 100 Hz  Range of the A/D converter: ±5 V You have to acquire these four signals  Sine wave with frequency 8.84 Hz, Amplitude 2 V  Sine wave with frequency 175 Hz, Amplitude 1 V  Sine wave with frequency 10 Hz, Amplitude 6 V. For each signal:  Identify the best window (Hanning – rectangular) for reducing or avoiding the leakage  Plot the spectrum modulus. 1.2 Example 2 Your acquisition system is configured as follows:  Sampling rate: 500 Hz  Number of samples: 2500  Antialiasing Filter Cut-off frequency: 150 Hz  Range of the A/D converter: ±5 V You have to acquire these four signals  Sine wave with frequency 1408.84 Hz, Amplitude 2 V  Sine wave with frequency 187.5 Hz, Amplitude 1 V For each signal:  Identify the presence of leakage, aliasing or clipping errors  Identify the best window (Hanning – rectangular) for reducing or avoiding the leakage  Plot the spectrum modulus. 1.3 Example 3 Your acquisition system is configured as follows:  Sampling rate: 5000 Hz  Number of samples: 10000  Antialiasing Filter Cut-off frequency: 2150 Hz  Range of the A/D converter: ±5 V You have to acquire these four signals  Sine wave with frequency 237.199 Hz, Amplitude 2 V  Sine wave with frequency 280.5 Hz, Amplitude 1.2 V  Sine wave with frequency 12287 Hz, Amplitude 1 V  Sine wave with frequency 4 Hz, Amplitude 52 V. For each signal:  Identify the presence of leakage, aliasing or other measurement errors; …