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1. (a) A sine wave at frequency f= 90 Hz is sampled digitally at sampling frequencies fs=200,160 and 50 Hz respectively. For each case, discuss whether there is aliasing. Also for each case, calculate the aliasing (perceived) frequency.(b) Using EXCEL (or Matlab or any other computer program) generate a sine wave at 90 Hz, DC offset =1.0 V, and amplitude = 2.2 V. Plot a smooth curve representing the real signal. Plot the time axis from 0 to 0.2 seconds, and the vertical axis from -2 to 4 V. On the same plot, plot the digitally acquired data (at 50 Hz sampling frequency) as symbols connected by straight line segments. Calculate the observed frequency from your plot and compare with the frequency calculated in part (a) and discuss briefly.
2. The signal-to-noise ratio SNR is defined as SNR=20log(Vsignal/Vnoise).(a) Calculate the signal-to-noise ratio SNR of an 80 Hz electrical signal with amplitude 2.00 V containing noise at 3600 Hz with amplitude 0.150 V.(b) In order to reduce the noise level the signal is filtered using a 2nd-order low-pass filter with a cutoff frequency of 100 Hz. Calculate the signal-to-noise ratio (SNR) with the filter and compare with part "a".Does the filter significantly improve the SNR?
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