The following signal is sampled by 12-bit ADC triggered by timer TIM7. The timer clock frequency is 80 MHz. The value of TIM7_PSC register is 79. The value of TIM7_ARR register is 99. Assuming that sampling starts at t = 0, determine the value of the sample x[80].
x(t) = 1.5 + 0.6sin(70t
To determine the value of sample x[80], we need to calculate the time at which the 80th sample is taken.
First, calculate the period of the timer:
Timer frequency = Timer clock frequency / (PSC * ARR)
Timer frequency = 80 MHz / (79 * 100)
Timer frequency = 10101.0101 Hz
Next, calculate the time between two samples:
Sampling period = 1 / Timer frequency
Sampling period = 1 / 10101.0101
Sampling period = 0.00009899 seconds
Now, calculate the time at which the 80th sample is taken:
Time = Sampling period * 79 samples
Time = 0.00009899 * 79
Time = 0.00781121 seconds
Now, substitute this time into the signal equation x(t) to get the value of x[80]:
x[80] = 1.5 + 0.6sin(70*0.00781121)
x[80] = 1.5 + 0.6sin(0.5467847)
x[80] = 1.5 + 0.6 * 0.5115554
x[80] = 1.5 + 0.30693324
x[80] = 1.80693324
Therefore, the value of sample x[80] is approximately 1.8069.