Signal acquisition

A/D conversion

Sampling rate  Nyquist-Shannon sampling theorem: If bandlimited signal x(f) holds in [-B;B], then if f s = 1 / T  2B then x k  x(t), meaning: the original signal can be transformed from the digitised signal without loss of information

Quantization  Ensures the adequate resolution of the digitised signal E.g.: 32bit ADC  2 32 = 4.3*10 9 level  coupled to a ±5V range this means a 0.23 nV precision! (16bit  levels  0.15mV precision) ( 8bit  256 levels  39mV precision)

Noise 1 – Quantization errors  Quantization = rounding  measurement error  Error limit: |  |<  / 2 (in case of linear q.)  Amplitude constantly between two q. levels: granular noise  Signal elevation faster than q. levels could follow: overload noise

Noise 2 – 50/60Hz Electric field  perpendicular Magnetic field

Noise 3 – Different ranges

Noise reduction - averaging  Very efficient on time-locked signals (EP epochs, spikes, oscillations,…)

Noise reduction - averaging  Cutting a signal to epochs  locked to a phenomenon (peaks, stimuli, …)  Threshold specification  manual  semi- and fully-automatic (by mean & SD)  Peak detection  threshold crossing (simple&fast but misleading)  detection of local maxima (minima)

Noise reduction - averaging

Noise reduction via spectral analysis

 Fast Fourier transform: efficient algorithm to compute the discrete Fourier transform and its inverse: TIME DOMAIN FREQ. DOMAIN Signal: FFT i-FFT

Noise reduction via spectral analysis  Noise reduction by filtering in the freq. domain: SIGNALFFT Noisy : Filtered :

Additional analyses in the frequency domain Periodogram Spectrogram Original signal

Seeking correlation between two datasets  Peri-Event Time Histogram ECG Blood flow