GB1494476A - Fourier analysers - Google Patents

Abstract

1494476 Spectral analysis IMPERIAL METAL INDUSTRIES (KYNOCH) Ltd 13 Nov 1974 [13 Nov 1973] 52534/73 Heading G1U [Also in Divisions G4 and H3] Apparatus in which a smoothed estimate of the spectral density function of a time series, such as f(t), Fig. 5, is calculated digitally using Bartlett's smoothing method, namely the method in which a record of length T is subdivided into T/# smaller segments each of length #, a sample spectrum is computed for each of the T/# segments, and all the sample spectra so obtained are averaged, is characterized in that means are provided whereby the number of segments and their duration can be adjusted so as to fit any given record length T, and in that once these parameters are set the cutoff frequency of an anti-alias filter is set automatically. As described all calculations are performed digitally and a read-only memory is used to produce the required sine and cosine values. An input waveform f(t), Fig. 5, is appropriately amplified (or attenuated) 10, Fig. 1, passed via an antialias filter 110 (see Division H3) to a sample and hold circuit 17, and each sample is digitized 19. When data above a minimum value Y set on switches 23 arrives, a control signal D initiates the analysis. All the digitized samples relating to one segment are entered serially into one of two circulating shift registers 24, 25 (each being 1,024 stages long and 9 bits wide), Fig. 2, so arranged that while one register is being written into with new samples the other is recirculated at a much higher rate to make available repeatedly all the samples from the immediately preceding segment. As the samples from the preceding segment become available they are applied, in parallel, to two multipliers 27, the other inputs of which receive appropriate sine and cosine values from a readonly memory 28, the result being that for each complete cycle of the samples of the preceding segment the functions - and are computed by accumulators 29 and 290 respectively, where x(n) are the sample values, N is the number of samples (=1,024 as described) and k is the argument, k being augmented by unity after each cycle of the store. For each value of k, these functions are squared 30, 300, and added 310, so as to provide in sequence the values of the sample spectrum associated with the preceding segment, and these values are stored in a circulating accumulator 31, Fig. 3, arranged so that as the values of the sample spectrum for the next segment occur they are appropriately added to the values already obtained, and finally the resulting totals are shifted to produce the required averages. These resulting values can be recorded logarithmically (characteristic and mantissa) 32, converted to analogue form 33 and suitably displayed. Whilst the analysis is proceeding, the averaging circuit is arranged to produce an approximation to a running average by dividing the current total by the nearest number of the form 2<SP>r</SP>, r = 0, 1, ..., to the number of segments currently processed. As described, the number of segments can be selected to be any number of the form 2<SP>a</SP>, a = 1, 2, ..., (so that the averaging can be effected by a simple binary shift by a places), and the number of samples per segment N is fixed. Thus, an operator, knowing the total duration T of the record to be analyzed, can compute the maximum detectable frequency, namely N2<SP>a</SP>/T, which he then sets on switches (15), Fig. 4, (not shown). These switches then set the sampling frequency (at four times the maximum frequency) and the cut-off frequency for the anti-alias filter.