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 this sample is obtained and then substitute it into the given signal equation.
The timer clock frequency is 80 MHz, and the value of the TIM7_PSC register is 79. This means that the timer clock frequency after the prescaler is 80 MHz / (79 + 1) = 1 MHz.
The value of the TIM7_ARR register is 99, which means that the timer will count up to 99 + 1 = 100 before it overflows and triggers the ADC.
The sampling frequency can be calculated by dividing the timer clock frequency by the timer period:
Sampling frequency = Timer clock frequency / (TIM7_ARR + 1)
Sampling frequency = 1 MHz / (100 + 1)
Sampling frequency = 10 kHz
The time interval between each sample is the reciprocal of the sampling frequency:
Sample interval = 1 / Sampling frequency
Sample interval = 1 / 10 kHz
Sample interval = 0.0001 seconds
To find the time at which sample x[80] is obtained, we multiply the sample interval by the sample index:
Time for sample x[80] = Sample interval * 80
Time for sample x[80] = 0.0001 seconds * 80
Time for sample x[80] = 0.008 seconds
Now we can substitute this time into the given signal equation:
x(t) = 1.5 + 0.6sin(70t)
x(0.008) = 1.5 + 0.6sin(70 * 0.008)
x(0.008) = 1.5 + 0.6sin(0.56)
x(0.008) = 1.5 + 0.6(0.533)
x(0.008) = 1.5 + 0.32
x(0.008) = 1.82
Therefore, the value of sample x[80] is 1.82.