Extraction of signals from noise

This chapter presents certain simple methods for describing mathematically some of the types of signals which are encountered in biomedical research. Techniques are described for both periodic and aperiodic signals. Techniques for extraction of signals from noise are also presented. Signal description and not data reduction is the theme of this chapter. For techniques directed toward statistical analysis of data, the reader is referred to standard reference works (for example, Wortham and Smith, 1959). 

Fig. 14. Extracting distinguishing features from noise pulse signal. Wavelet coefficients in shaded regions represent stable extrema, (a) Wavelet decomposition of noisy pulse signal (b) wavelet decomposition of pulse signal. (Reprinted from Bakshi and Stephanopoulos, Representation of process trends, Part III. Computers and Chemical Engineering, 18(4), p. 267, Copyright (1994), with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.)...

Chimg, SH and Kennedy, RA, Forward-backward non-linear filtering technique for extracting small biological signals from noise. Journal of Neuroscience Methods 40 (1991) 71-86. 

The term is used in AMDIS in the broad sense of extracting one signal from a complex mixture. The treatment of noise, the correction for base line drift, and the extraction of closely co-eluting peaks from one another are part of the deconvolution process. 

There is significant debate about the relative merits of frequency and time domain. In principle, they are related via the Fourier transformation and have been experimentally verified to be equivalent [9], For some applications, frequency domain instrumentation is easier to implement since ultrashort light pulses are not required, nor is deconvolution of the instrument response function, however, signal to noise ratio has recently been shown to be theoretically higher for time domain. The key advantage of time domain is that multiple decay components can, at least in principle, be extracted with ease from the decay profile by fitting with a multiexponential function, using relatively simple mathematical methods. 

Background copper levels in seawater have been measured by electron spin resonance techniques [300]. The copper was extracted from the seawater into a solution of 8-hydroxyquinoline in ethyl propionate (3 ml extractant per 100 ml seawater), and the organic phase (1 ml) was introduced into the electron spin resonance tube for analysis. Signal-to-noise ratio was very good for the four-line spectrum of the sample and of the sample spiked with 4 and 8ng Cu2+. The graph of signal intensity versus concentration of copper was rectilinear over the range 2-10 xg/l of seawater, and the coefficient of variation was 3%. 

---