Design and application of binary sequences with optimised lowpass properties

It is shown that binary sequences having prescribed spectral properties may be designed by an optimisation procedure based on a delta-modulation algorithm. The method is specifically applied to the design of lowpass sequences of lengths 128,256 and 512 bits which, after a simple integration process, exhibit spectral properties related to type-2 nonrecursive-digital-filter impulse responses. Highpass sequences can be obtained by a simple transformation. The limitations of the procedure and the implications of quantisation error are discussed. A theoretical prediction is obtained for the smallest sequence length necessary to achieve a given spectral bandwidth. Applications include digital filters, which can be simply implemented by digital hardware performing primitive arithmetic operations.