Using the time domain for analog signal representation

There is an ever-growing interest within the fields of neurophysiology—as well as within coding theory and signal processing—into the particular information transmission method employed by most neurons: spikes. Many models used today regard those voltage pulses as uniform events where only the occurrence of an event from a particular neuron at a particular moment in time matters. This signal representation offers many powerful encoding schemes, where information can be encoded into spike-event patterns over time and space. An analog value, for instance, can be encoded as an interval between two spikes. Time-domain encoding and processing can also be used to advantage in electronic devices. So, besides representing signals with currents or voltages, they can just as well be represented with time intervals. This is, of course, not unknown in analog electronics, but since time-domain signals also consume time, they are not widely popular. They do, however, start to be increasingly important in neuronal models and, thus, in neuromorphic electronics. The concept is not just limited to the imitation of biological functions, but can also be applied to more classical computations. Let us consider two simple examples for an analog division and multiplication circuit. A voltage can be divided by a current by measuring the interval it takes to deplete a capacitor from that voltage down to a zero reference. The output of that circuit is then that time interval, represented (for example) by a pulse width (first stage in Figure 1). Alternatively, a current can bemultipliedwith an interval by integrating that current on a capacitor during that interval. Thus, the output can be read as the voltage on that capacitor (second stage in Figure 1). These two stages in sequence can be described as an amplifier with voltage input and output: it samples the input voltage when triggered (signal g), and its gain A is set by the ratio of two bias currents Figure 1. A voltage amplifier with internal time-domain representation.