Patent GB-1475601-A (GB)
Title: Digital spectrum analyzer
IPC: G01R23/00
Filed: 1974-05-14
Abstract: 1475601 Spectrum analyzer SANGAMO WESTON Inc 14 May 1974 [14 May 1973] 21389/74 Heading G1U [Also in Division G4]  A spectrum analyzer multiplies each word of one of a series of p sequences each of N digital words representing an analogue signal, e.g. a vibration transducer output, with a selected window function, combines each product with a series of sine and cosine functions, the functions of each series being of a series of arguments each including a value representing a respective one of a series (K) of spectral lines, to produce, respectively, a series of N words I and a series of N words R representing, respectively, the imaginary and real parts of discrete Fourier transforms of the products for the series of spectral lines, accumulates for each spectral line the associated N words I and N words R to produce averages thereof, and generates for each spectral line the sum of the squares of the corresponding averages to produce a value representing the power value Xk of the spectral line. Each of the series of sequences of digital words is processed as above to produce power values Xk,p and the p results for each line are averaged in one or in two modes. An analogue input is amplified, filtered &c. and fed to an analogue to digital converter after the addition of a statistically distributed noise signal (see below) to produce sequences of N, e.g. 1024, words representing the signal which are stored in a circulating memory. The output of the memory is connected to a multiplier where the words are multiplied with a selected window function and the products are stored in a circulating memory. A memory storing several window functions is provided, e.g. a Hanning function, and one function is selected. The stored products of each sequence are counted by an n-counter and are all fed to a sine/cosine function multiplier for each of a number of K values counted by a K- counter and each representing a different spectral line. The current n and K counts are used, after suitable manipulation, Fig. 8 (not shown), to address a read only memory which provides the appropriate sine and cosine functions to the multiplier. The memory stores a series of a single function e.g. a sine function, for a single, quadrant, the other, cosine, function and the functions for other quadrants being obtained by appropriately addressing the memory and manipulating the resulting output. The resulting N values R and N values I are for each value K averaged, and the average values are squared and added to produce a power value X k . By processing a series of p sequences, e.g. 1024, each of N words as above a series of p values for the power value for each K, X k,p  are obtained and these are averaged in a sum or an exponential mode. Sum mode averaging: The p power values for each spectral line K are averaged in accordance with the algorithm p<SP>-1</SP>2<SP>b</SP> (a Y k , p-1 + 2<SP>-b</SP>X k,p  where p is the number of the power value currently being operated on, Yk, p-1 in the value of the expression in parenthesis prior to the current value being operated on, Xk,p is the power value currently being operated on, b is an integer where 2<SP>b-1</SP> < p # 2<SP>b</SP>, and a is 1/2 if p-1=2<SP>b-1</SP> and 1 otherwise. The algorithm is performed by the apparatus shown schematically in Fig. 9 (not shown), the bracket calculation for each value p being produced by adder 134 and recirculated via memory 98 for addition for the next value of p. A p counter 126 keeps track of the number of values processed and the final result is obtained from log converter and adder 140. Exponential mode averaging: Following a sum mode averaging operation the power values for each spectral line K may also be averaged in accordance with the algorithm: Y k , p-1 + 2<SP>-c</SP> (X k , p-Y k , p-1) where C in the log of the number of spectra averaged during the sum mode averaging and the remaining terms are as in sum mode averaging and are derived from the sum mode averaging apparatus. Analogue to digital conversion: To improve the resolution of the conversion (which is itself not described) a statistical noise signal is added to the analogue input prior to sampling. The converter produces M bit digital representations of the analogue signal which is sampled at a frequency Fs which is four times the highest frequency of the range being analysed. The arrangement  extends the resolution to less than A m  2<SP>-M</SP>, where A m  is the full scale input signal, by using a white noise signal with a probability density function which is zero except over the interval A m (-2<SP>-(M+1)</SP>) to A m (+2<SP>-(M+1)</SP>) where it is essentially constant at 2<SP>M</SP>/Am and with a power density spectra which is zero over the intervals Q.F s  - Fm to Q.F s  + Fm for Q = 0, 1, 2,... where Fm is the maximum signal bandwidth and the sampling frequency is QFm. The redundant information resulting from the samples, i.e. each sequence of Q/2 samples are averaged to produce the required number of samples over a given interval t, i.e. 2Fmt. The noise signal is produced by adding two square waves, one at a frequency Fs/2 and the other at Fs/4, and the output of a normally distributed white noise generator.