The following signal is sampled by 12-bit ADC triggered by timer TIM6. The timer clock frequency is 80 MHz. The value of TIM6_PSC register is 7. The value of TIM6_ARR is 112. Determine the sampling frequency fs. Explain if this sampling frequency is sufficient to avoid aliasing. Show your work.
To determine the sampling frequency, we first need to calculate the timer frequency (TIM6) using the following formula:
TIM6 frequency = Timer clock frequency / ((TIM6_PSC + 1) * (TIM6_ARR + 1))
TIM6 frequency = 80 MHz / ((7 + 1) * (112 + 1))
TIM6 frequency = 80 MHz / (8 * 113)
TIM6 frequency = 80 MHz / 904
TIM6 frequency ≈ 88.49 kHz
Since the ADC is triggered by timer TIM6, the sampling frequency (fs) will be the same as the timer frequency:
fs = 88.49 kHz
In order to avoid aliasing, the sampling frequency should be at least twice the maximum frequency component present in the signal. This is known as the Nyquist-Shannon sampling theorem.
If the maximum frequency component in the signal is fmax, then the Nyquist frequency (fNyquist) would be:
fNyquist = 2 * fmax
In order to avoid aliasing, the sampling frequency fs should be greater than fNyquist. In this case, if the fmax is known, we could compare it to the sampling frequency fs to determine if aliasing will occur.
Is this correct?
I apologize for the oversight in my previous response. Let's correct the calculations and determine if the given sampling frequency is sufficient to avoid aliasing.
The correct calculation for the timer frequency (TIM6) is as follows:
TIM6 frequency = Timer clock frequency / ((TIM6_PSC + 1) * (TIM6_ARR + 1))
TIM6 frequency = 80 MHz / ((7 + 1) * (112 + 1))
TIM6 frequency = 80 MHz / (8 * 113)
TIM6 frequency = 80 MHz / 904
TIM6 frequency ≈ 88.50 kHz
Therefore, the correct sampling frequency would be:
fs = 88.50 kHz
To determine if this sampling frequency is sufficient to avoid aliasing, we need to apply the Nyquist-Shannon sampling theorem which states that the sampling frequency should be at least twice the maximum frequency component in the signal (fmax) to avoid aliasing.
If we know the maximum frequency component (fmax) in the signal, we can compare it to the Nyquist frequency (fs/2) to determine if aliasing would occur. If fmax is less than fs/2, then the sampling frequency fs is sufficient to avoid aliasing.
If you provide the maximum frequency component (fmax) in the signal, we can perform the comparison to confirm if the given sampling frequency is indeed sufficient to avoid aliasing.