Speech:

Software Algorithm and Hardware Design for Real-Time Implementation of New Spectral Estimator

Abstract
Frequency analysis is important to biomedical engineering for the quantitation of medical signals and images. However, the most commonly used methods, the Fourier transform and the Wavelet transform, are composed of bases which lack biophysical meaning. The standard Fourier basis consists of a series of sinusoids, which rarely if ever convey the shape of repetitive patterns present in biomedical data. Similarly, the mother wavelet used for Wavelet analysis is selected from a library of candidate mother wavelets that has been developed over the past two decades and have no known biophysical meaning. Neither the Fourier transform nor the Wavelet transform is conducive to real-time calculation. This is due to the complex nature of their implementation and the need for a recalculation of most or all steps on each successive iteration. However, implementation of a real-time system for frequency analysis would enable content evolution to be evaluated at the maximum time resolution, i.e., every sample point. Such information would be valuable to detect spectral transients, and to understand the temporal evolution in the frequency content, including the appearance and disappearance of components, presence and absence of split frequency peaks, and the temporal relationship between spectral peaks. Often, it is also desirable to evaluate multichannel data, which can make real-time implementation difficult or unachievable with current computational power.

We have developed a new spectral estimator (NSE) with characteristics that are advantageous for biomedical analyses as compared with Fourier and Wavelet analysis. The NSE basis is data-driven and is calculated from signal averaging; thus the components have a biophysical basis. Real-time update can be done with minimal calculation by using moving signal averages. An algorithm for this purpose was devised and tested on clinical data from 216 fractionated atrial electrogram sequences. The digital sampling rate was 977 Hz, or approximately 1 millisecond between sample points. The real-time NSE power spectra were generated for 16,384 consecutive data points in the signals. The same clinical data was used for spectral calculation using a radix-2 implementation of the discrete Fourier transform. The NSE algorithm was also implemented as a real-time spectral analyzer electronic circuit board.

The results of testing showed that the average interval for a single real-time spectral calculation in software was 3.29 μs for NSE versus 504.5 μs for the Fourier transform. Thus the NSE algorithm was found to be 150× faster than the Fourier method. Over a 1 millisecond sampling period, it was determined that the NSE algorithm could analyze a maximum of over 300 data channels, while the fast Fourier transform could only be used to analyze a single data channel. Furthermore, for eight second sequences, the NSE spectral resolution in the 3-12 Hz range was 0.037 Hz while the Fourier spectral resolution was only 0.122 Hz, about ¼ of the NSE resolution. The NSE was also implemented as a standalone spectral analyzer board using less than 30 integrated circuits at a cost of slightly over $500.

Based on the findings, the NSE real-time algorithm was shown to have low computational cost and complexity, and can be implemented in both software and hardware for 1 millisecond updates of multichannel spectra. This can be useful both for detection of transients and trends in spectral components, as well as to obtain a snapshot of the frequency content at any time epoch. Moreover, it can also be useful retrospectively to rapidly analyze big data for which it is desirable to calculate the frequency spectrum at all discrete time points, so that spectral transients and trends can be determined.