# Can measure the rms level the background noise

Integrated Amplifier Architectures for Efficient Coupling to the Nervous System 175

**3 Efficient Signal Processing: Adaptive Neural Spike
Detection**

*A. Adaptive Spike Detection Algorithm*

The goal of our spike-detection algorithm (first described in [41]) is to adaptively set a detection threshold that is low enough to capture action potentials, but high enough to reject occasional peaks in the background noise. We assume Gaussian background noise having a mean of zero. (Measured background noise from actual neural recordings has a roughly Gaussian distribution, though the tails are slightly wider [42].) Therefore the noise is entirely described by its rms value, which is equivalent to its standard deviation, �. If we can measure the rms level � of the background noise, we can set a threshold to some multiple of � and reject all but a vanishingly small fraction of the background noise. For example, with a threshold of 5�, the probability of Gaussian noise triggering the spike detector is approximately 3 × 10−7.

To develop a simple method for measuring �, we observe that if a threshold is set at �, the probability of Gaussian noise exceeding this threshold is 0.159. Figure 7(a) shows a noise waveform and a threshold level of 1 �. After comparing the noise with this threshold, we get a digital waveform having a duty cycle (i.e., the fraction of time the waveform is high) of 0.159 [see Fig. 7(b)]. The duty cycle is proportional to the dc level of this digital waveform, and we can use this signal as feedback to servo a reference voltage to the 1 � level of the waveform.

Fig. 8 Block diagram of the adaptive
spike detectionalgorithm |
vin | comparator A | 0.159 | ||
---|---|---|---|---|---|

V1 σ | duty cycle |
||||

K | |||||

N | comparator B | ||||

VN |