1. A continuous signal is monitored with LabVIEW, the figure on the right shows the continuous signal acquired with a sufficiently high sampling rate to represent it correctly while the FFT magnitude vs. frequency shows the frequency content from a sampling of the signal at sampling rate (fs) less than the Nyquist frequency requirement. Determine the following 5.5 The input signal frequency, fm a. 02 04 06 08 Time b. The sinusoid equation that describes input signal: c. What should be the lowest sampling frequency, f, to satisfy the Nyquist Theorem to correctly capture the frequency information of the input signal? FFT d. Does the FFT result show an alias frequency fa or the correct signal frequency fm? i. if yes T i. if no fm= Freq. [Hz] be if fm is the value What would the alias frequency found for part a (show your calculations for each) 2. An electrical (RC) circuit which can be modeled as a 1^ft order system is initially at 0.05 VDC due to the capacitor not being fully discharge. At time, t=0 sec, the supply voltage (Vs) is switched on to 5VDC. A voltmeter monitors the voltage across (Vo) the capacitor and at time, t=2 seconds, it records a voltage of 2.5 VDC Assume the voltmeter has a faster response time than the RC circuit. the input signal and the estimate of the circuit’s response w.r.t. time. What is the circuit’s time constant, x? How long would it take for the voltage across the capacitor to reach 4.5 Volts?

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