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].
bx(t) = 1.5 + 0.6sin(70t
First, let's determine the sampling frequency. The timer frequency is given by:
f_timer = timer_clock / (TIM7_PSC + 1)
f_timer = 80 MHz / (79 + 1)
f_timer = 1 MHz
Next, let's determine the sampling period, which is the time between samples, given by the timer:
T_sampling = (TIM7_ARR + 1) / f_timer
T_sampling = (99 + 1) / 1 MHz
T_sampling = 100 / 1 MHz
T_sampling = 100 * 10^(-6) s
T_sampling = 100 µs
Now, let's find the time when the 80th sample is taken:
t_80 = 80 * T_sampling
t_80 = 80 * 100 µs
t_80 = 8000 µs
Now we can determine the value of the sample x[80]:
x[80] = bx(t_80)
x[80] = 1.5 + 0.6 * sin(70 * t_80)
Let's calculate the value:
x[80] = 1.5 + 0.6 * sin(70 * 8000 * 10^(-6))
x[80] ≈ 1.5 + 0.6 * sin(0.56)
x[80] ≈ 1.5 + 0.6 * 0.527
x[80] ≈ 1.817
Now let's scale this value to a 12-bit number, which ranges from 0 to 4095:
scaled_x[80] = 4095 * (x[80] - x_min) / (x_max - x_min), where x_min = 1.5 - 0.6;
x_max = 1.5 + 0.6 (since sine ranges from -1 to 1)
scaled_x[80] = 4095 * (1.817 - 0.9) / (2.1 - 0.9)
scaled_x[80] ≈ 4095 * 0.917 / 1.2
scaled_x[80] ≈ 3131.08
Since ADC values are integer numbers, we'll round it:
Final value of the sample x[80] ≈ 3131