The Shannon information measure was developed as a way to quantify the capacity and ability of a communication channel to transmit signals, to measure with how much certainty the receiver would get a particular output for a given input signal on the transmitter end. Conversely, one can then measure the certainty that a particular input signal was transmitted given the output signal received on the receiver end.
To understand mutual information, the concept of entropy needs to be explained:
In theory, mutual information would allow us to test different hypotheses for neural encoding, compare information encoded by different subpopulations of neurons, and measure the effect of different signal processing techniques. However, calculating mutual information poses different computational challenges.
I have been involved with some pre-amplifier testing, but my primary involvement in the development of our pre-conditioning hardware has been in the design of switched capacitor filters.
Performing real-time processing of neural signals from freely-behaving animals requires an implantable integrated circuit (IC) chip. Such a chip would allow electrical signals from the brain to be acquired and processed and for the output control signals to be transmitted through RF telemetry to some external prosthetic device. The raw signals acquired by the neuro-chip from the recording electrodes will be contaminated by both high frequency electrical noise as well as low frequency noise from unwanted activity of the animal, such as breathing and chewing. Thus, an integrated bandpass filter is needed to obtain the signals in the desired frequency range, which for the neural signals of interest lies primarily between 500 and 5000 Hz. Traditional bandpass filters contain resistors and capacitors, the values of which determine the characteristics of the freuquency response. However, to implement the filter economically and practically, the values of the resistors and capacitors, which are directly proportional to the component areas in silicon, must fall in a certain range. The desired cutoff frequencies mandate unreasonably large values. Furthermore, as capacitor values are lowered into feasible ranges, resistor values are inherently pushed farther out. A switched capacitor is a capacitor of value C that is connected to different voltage nodes on alternate halves of the switching period and acts analogously to a resistor of value 1/fC, where f is the switching frequency. Thus, switched capacitors can reduce the area of the filter enough to be implemented on a chip that can be implanted in the brain.
Traditional bandpass filters contain resistors and capacitors, the values of which determine the characteristics of the freuquency response. However, the resistor and capacitor values needed to meet the desired bandpass specifications for the filtering of neural signals would be too large to be implemented economically and practically in an implantable IC chip. Switched capacitors offer a viable solution, as they can replace resistors with capacitor values which are inversely proportional to the resistor values to be simulated. An 8-pole Butterworth bandpass filter consisting of four cascaded Sallen-Key biquadratic filters was designed, and simulations showed the design to meet the bandpass specifications. Although switched capacitors alleviated the problem of excessively large capacitor values, and thus areas, the bandpass filter requires the largest capacitor to be two orders of magnitude larger than the smallest capacitor. These preliminary results show that an alternative design must be found to implement the filter efficiently. A Chebyshev bandpass filter implemented in a switched capacitor design by applying the bilinear transformation to the desired transfer function has been proposed as the design of choice. A fourth-order version of this filter will be designed to meet the specifications for the biomedical application, and upon successful simulation, will be layed out and fabricated.