Question

If you have an EEG (Electroencephalogram) signal with a range of 0 - 40 Hz and amplitude range of 5 - 300 µV, and you are using an analog to digital convertor (ADC) and you want a resolution of at least 0.05 µV/bit:

a.) Calculate the minimum bit size of the ADC. What should be your minimum sampling frequency and sampling interval to avoid aliasing?

Answer 1

The minimum bit size of the ADC should be 13 bits. The minimum sampling frequency to avoid aliasing should be 80 Hz, and the sampling interval should be 12.5 milliseconds.

Step-by-step explanation:

a.) To calculate the minimum bit size of the ADC, we need to consider the desired resolution of 0.05 µV/bit. The voltage range of the EEG signal is 5 - 300 µV. The minimum bit size can be calculated using the formula: Bit Size = log2((Voltage Range) / (Resolution)) = log2((300 µV - 5 µV) / (0.05 µV)) = 12.96 bits. Hence, the minimum bit size of the ADC should be rounded up to 13 bits.

b.) To avoid aliasing, the sampling frequency should be at least twice the highest frequency in the signal, according to the Nyquist-Shannon sampling theorem. In this case, the highest frequency is 40 Hz. Therefore, the minimum sampling frequency should be 2 * 40 Hz = 80 Hz.

c.) The sampling interval can be calculated using the formula: Sampling Interval = 1 / Sampling Frequency = 1 / 80 Hz = 0.0125 seconds, or 12.5 milliseconds.