692 BARBER AND TUCKER [CHAP. 19 



amplitude of the components is weighted by a "filter-function", or response- 

 curve, which is maximum at the centre frequency and is negligibly small out- 

 side certain limits. The "band-width" of the filter is usually defined as the 

 frequency difference between the points at which the response falls to half (in 

 terms of mean-square amplitude). 



If L is the length of the record in seconds, it can be shown to be completely 

 represented by the sum of harmonic components with frequencies separated by 

 IjL c/s. This is, therefore, the limit of useful resolution of the analysing system, 

 and is fundamental to a finite recording. In "periodogram" methods of analysis, 

 the amplitude of these individual harmonic components is measured, but they 

 show enormous random fluctuations (the standard error is 100%) and have to 

 be smoothed to reduce these before they can be used. Other methods use a 

 filter with a comparatively wide pass-band in the first place. The advantage of 

 the periodogram method is that it gives the maximum possible resolution, and 

 the amount of smoothing permissible without loss of detail can be estimated 

 by inspection. The wide-band methods have the advantage of reducing the 

 amount of human time and thought necessary, but occasionally significant 

 detail may be lost. 



Either type of analysis may be performed by analogue or digital methods, 

 but the present trend is towards the latter. The reasons for this seem to be : 



(1) A digital computer will usually give either the correct answer with a 

 high accuracy, or, if a fault occurs, an answer which is obviously wrong. 



(2) An analogue computer is a specialized piece of equipment which is not 

 readily adaptable. Thus, it requires a high capital outlay which may be wasted 

 if ideas change (for example, if higher accuracy is required). Suitable digital 

 computer programmes are usually available (but can be quite expensive if one 

 has to be developed specially), and most laboratories have access to a digital 

 computer and its associated equipment. 



On the other side of the balance, if an analogue machine is available, an 

 analysis can be performed quickly and cheaply, which can be a major advantage 

 if many routine analyses have to be performed. 



Analogue methods start with the record on photographic paper (e.g. Barber 

 et at., 1946) or on magnetic tape (e.g. Pierson and Chang, 1955). The photo- 

 graphic methods have the advantage that the record can be seen by eye, and 

 records can be prepared by hand if necessary. Magnetic tape methods seem to 

 be more flexible ; in particular, it is easier to vary the length of the record. The 

 records are run through a device which converts them to an electric signal at 

 103 to 104 times the recording speed, and passed through a filter whose output 

 is recorded. For periodogram analysis, the filter has to be extremely narrow 

 (see Tucker's description, 1956b, of a later version of the Barber et al. machine). 

 For wide-band analysis, Chang (1954) has calculated the optimum shape of the 

 filter function. To sweep the frequency range, the rate of reproduction may be 

 varied, as in the Barber et al. machine, or the frequency of the filter may be 

 varied, usually by a heterodyne system. 



