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 the sample x[80], we first need to calculate the sampling rate of the ADC based on the timer settings.
The timer frequency can be calculated as follows:
Timer frequency = TIM7 clock frequency / (TIM7_PSC + 1) = 80 MHz / 80 = 1 MHz
The sampling frequency will be the inverse of the timer period:
Sampling frequency = 1 MHz / (TIM7_ARR + 1) = 1 MHz / 100 = 10 kHz
Since the sampling starts at t = 0, the value of x[80] corresponds to the sample taken at time t = 80 / 10 kHz.
Substitute t = 80 / 10 kHz = 0.008 s into the original signal equation:
x[80] = 1.5 + 0.6sin(70*0.008) = 1.5 + 0.6sin(0.56) ≈ 1.5 + 0.6*0.5398 ≈ 1.5 + 0.3239 ≈ 1.8239
Therefore, the value of the sample x[80] is approximately 1.8239.