GB1366085A - Generation of hadamard transforms of electrical signals - Google Patents

Abstract

1366085 Digital transmission; coding BRITISH BROADCASTING CORP 12 July 1972 [13 July 1971] 32837/71 Heading H4P A signal such as a T.V. signal is coded for transmission using Hadamard transforms. The simplest Hadamard matrix is of the order 2<SP>1</SP> and is given by the next being of order 2<SP>2</SP> and given by and so on. The image to be coded is divided, by scanning, into a series of 16 elements A to S in the described embodiment and each element A, B, &c. consists of a binary number which has m(=4) bits and which represents a different sample of the image. A corresponding 16 x 16 Hadamard matrix can be produced from these 16 elements (and is given at Y in the Table in the complete Specification). The circuit illustrated produces at Ya signal element a, b, &c. for each row of the matrix, wherein a to s together represent the Hadamard (H16) transform of the input elements A to S. The first of the four stages (i=4) of the circuit consists of two 8-position shift registers 12, 18; the output signal of the first 12 having the input signal U (A to S) subtracted from it at 16 (the difference being fed to the second register 18), and added to it at 14, the sum being fed direct to a switch 20. The switch 20 is controlled by T4 to pass sequentially to V firstly the 8 sum elements from 14 (A+J, B+K, &c.), and secondly the 8 difference elements from 16 delayed by 8 element periods at 18 (A-J, B-K, &c.). The second stage (i=3) operates similarly but with only 4-position registers whose capacities are increased by one bit. Each sum and difference operation now produces a 4-element term at W. Similarly, in the third and fourth stages the shift registers have only 2 and 1 stages respectively, with correspondingly increased bit capacities and the sum and difference operations produce the evaluations of the 8-element and 16- element terms, the resultant at Y being thus 16 rows a to s of elements each row being the evaluation of 16 elements (i.e. a 16 x 16 matrix). Provided that the Hadamard matrix is symmetrical it is shown that the image information can be retrieved at a remote receiver by taking a further Hadamard transform of the received signal Y. If the elements A to S were samples of an analogue signal, rather than binary words, similar operations can be carried out to achieve the Hadamard transforms by replacing the shift registers with analogue clocked stores (e.g. bucket-brigade type), and using analogue sum and difference circuits.