13 07 20sol

Pagina 1

EXERCISE 1 It is required to design an analog to digital (A/D) conversion system to record EEG traces in adult participants using a 10-20 montage: a) Draw the block diagram of the A/D conversion. For each stage of the conversion, report the numerical values referring to the employed quantities. 𝑢𝑢(𝑡𝑡) is obtained by recorded scalp EEG activity on a subject by means of 10-20 EEG system. EEG Band 0.5-70 Hz Analogue filter is a low pass anti-aliasing filter (LPAA). A LPAA is a filter used before a signal sampler to limit the bandwidth of a signal in order to properly apply the sampling theorem. LPAA 𝑓𝑓 𝑐𝑐𝑐𝑐𝑐𝑐 is chosen to be equal to 75 Hz in to limit the bandwidth of the signal and not to lose the frequency content of the signal itself. A/D: Shannon theorem fulfilled so that 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠≥ 2𝑓𝑓𝑠𝑠𝑠𝑠𝑚𝑚, where 𝑓𝑓𝑠𝑠𝑠𝑠𝑚𝑚 is the maximum frequency content of a signal (after proper limiting the band of the signal). In this context, we choose 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠=150 Hz, 𝑓𝑓𝑁𝑁𝑁𝑁𝑁𝑁𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐=75 Hz. Quantization is defined upon the signal dynamic and quantization level employed, in terms of bits. Scalp EEG dynamic range is approximately 1mV (peak -to-peak) and we can choose a 12 bit to code the signal. Thus, each level of quantization q is equal to 1 𝑠𝑠𝑚𝑚 212 = 0.001 𝑚𝑚 4096 = 2 × 10−7𝑉𝑉= 0.2 𝜇𝜇𝑉𝑉 Numerical EEG is a discrete signal, discrete in both time and amplitude. b) Participants undergo a protocol consisting of 30- s eyes closed followed by 30- s eyes open. Identify a parametric or a non parametric spectral methodology to extract the PSD of the EEG signal. Apply it during the: a) the eyes closed and the b) eyes open phases. Report the specifications of: - your data length - PSD computation technique: frequency resolution, model order, window of observation, ... Given the…