Stochastic resonance (SR) is a phenomenon in which a weak signal and noise under a threshold are put into a nonlinear threshold type signal transfer system, such as a neuron, and transferred to the output at a level exceeding the threshold. Normally, noise will disrupt the signal transfer, but in a system with SR phenomenon, the signal-to-noise ratio (SNR) of the output is enhanced when there is noise of moderate intensity.
By using this principal, it is possible to detect a weak signal using noise. Figure 1(a) shows the time chart of when a weak signal and noise are added to a single nonlinear threshold unit that will pulse when the input exceeds the threshold value. When the input is only a weak signal, there will be no pulse because it does not exceed the threshold. When noise is included, the signal will exceed the threshold stochastically, generating a pulse (the arrow in the figure) and transferring the input information to the output. The probability of a signal exceeding the threshold will be greater with stronger noise, but the output will be disrupted if the noise intensity is too high; therefore, SNR will be a parabolic curve against the change in noise intensity, as shown in Figure 1 (b). Using this method for signal detection is not practical because it is necessary to tune the noise intensity to gain a high SNR.
On the other hand, analytical research using the computer simulation of Collins et al [Nature 367, 236 (1995)] shows that the SNR can be enhanced in a wide range of noise intensities by defining a nonlinear threshold unit with a SR phenomenon as an SR unit and placing them in parallel. This result shows the technological usability of the SR phenomenon. For example, when applied to a signal-detection system, the SR phenomenon can be used without tuning the noise intensity.
When actually applying the parallel SR unit to signal processing, it is necessary to conduct real-time processing with multiple units. Therefore, we developed a signal detection and analysis system using parallel SR units in the proposed system to detect weak audio signals and real-time analysis of I/O signal correlation.
With a parallel SR unit system, SNR will improve against a wide range of noise intensities with more parallel units. Therefore, to apply the parallel SR principal to signal processing, it is necessary to operate dozens of SR units in parallel.
When processing with a computer, the processing speed will slow down when there are too many SR units, so it is difficult to process high-speed signals with dozens of units operating in parallel. Using analog circuit SR units is one of the solutions, but it would be necessary to create as many SR units as the number of actual parallel units, which would be very time consuming and expensive. Furthermore, it is necessary to recreate the whole circuit to modify the system, and it is difficult to prepare noncorrelated noise for each channel for the same number of units.
To address these issues, we needed a system that could be structured like a program, operate in parallel like an analog electronic circuit, and supply multiple channels of noise.
The System Structure
To solve these issues, we developed a system configuration using the following hardware:
- An NI PXI-7852R reconfigurable FPGA multifunction data acquisition (DAQ) module
- An NI PXI-8106 controller
- An NI PXI-1042Q chassis
We used LabVIEW and the LabVIEW FPGA Module as the software platform. With FPGAs, we can operate program blocks in each SR unit in parallel with the internal clock. LabVIEW enables the creation of FPGA bit files in a graphical programming environment, thus enabling users to develop systems in a short period of time. Therefore, this type of system would best solve our issues. A block diagram of this system is shown in Figure 2.
The signal input from the analog input (AI) of the FPGA multifunction DAQ module is processed with parallel SR units in the FPGA, and the processed result outputs from the analog output (AO) without going through a host, creating a system that makes it possible to process the signal in real time within the audible frequency range. A noncorrelated noise created by the noise generator in the FPGA is an input for each unit. A weak audio signal under the SR unit threshold is an input into the data acquisition AI, and the system is configured so the audio reproducibility can be checked directly by headphones connected to the AO signal. The front panel of the FPGA target is shown in Figure 3.
There are six groups totaling 96 units, and we can set the parameters for the SR units by each group. One group consists of 16 SR units. The front panel for the host VI is shown in Figure 4. A slide can intuitively operate the parameters for the neuron units, and an automatic measurement can streamline the experiment using sequence control. The controllable input parameters include noise intensity, the threshold of the neuron, the number of parallel SR units, and the output level adjustment.
The input and output waveforms are transferred to the host using direct memory access (DMA) and can be monitored in real time on a graph display. Also, we can analyze the correlation between the I/O signals against noise intensity in real time, making it possible to reduce the analysis time. We can record the input and output waveforms with a maximum sampling rate of 750 kS/s, making offline analysis possible.
With this system, we can use 96 parallel SR units with the FPGA noise generator to supply 96 channels of noncorrelated noise. Also, it has drastically reduced the time needed to modify the system. With a system of conventional analog electronic circuits, it would take more than 10 hours to modify four elements; however, with this system the time it takes to modify 96 units is reduced drastically to mere minutes, enhancing the throughput of the research.
When we used and analyzed a sinus signal with a frequency range of 20 Hz to 20 kHz and amplitude lower than the threshold, we confirmed that a signal in audible range can be detected in real time and it is possible to use the system for a nonperiodic signal such as music. We clearly measured the advantage of improving SNR in various noise intensities, which is the benefit of making the SR units parallel. We resolved all of the initial system development issues.
We used the NI PXI-7852R for the signal detection and analysis system with parallel SR units, which made real-time processing possible. We can apply this configuration to systems detecting audio signals as well as signals from different sensors. Furthermore, by using the NI PXI-7854R or increasing the number of boards, we can increase the number of SR units, enabling us to further expand our research.
The Institute of Scientific and Industrial Research, Osaka University