The frequency of an exponentially decaying wave is estimated

The frequency of an exponentially decaying wave is estimated to be 20Hz. What sample rate and how many data points shall we have to record 30 complete cycles with 15 points in each cycle? 200 samples/sec and 300 samples in total 300 samples/sec and 450 samples in total 300 samples/sec and 300 samples in total 200 samples/sec and 450 samples in total How many data points do we need to capture the system for the first 4 seconds using the same sampling rate calculated above? 1200 samples 800 samples 1600 samples 1800 samples

Solution

T = 1/f = 1/20

Since there are 15 points in each cycle and the cycle is of 1/20 seconds

Hence number of samples = 15/(1/20) = 300 samples/seconds

Number of samples = 30 complete cyles * 15 points/complete cyles = 450 samples in total

Hence correct answer is Option B

b)

Data points need to capture = 300 samples/second * 4 seconds

=> 300 * 4

=> 1200 samples

Hence the correct answer is Option A