Impulse-Equivalent Sequences and Arrays

Matthew Ceko, Mustafa Hamid, Imants Svalbe, Timothy Petersen, Andrew Tirkel

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch


The delta function is important in discrete signal and image processing as it is the exemplary perfect point spread function in the spatial or time domain. It provides 100% contrast resolution for all frequencies up the Nyquist frequency in the Fourier domain (perfect modulation transfer function). The construction of spatially finite discrete functions that mimic these properties of the delta function becomes of great value when we want to synchronise signals in time or localise patterns in space. Equivalently, sparse binary arrays are templates for spectrally-neutral functions that provide unbiased sub-sampling patterns for compressed sensing applications. Here a method is described that constructs exact, impulse-equivalent functions by combining complementary sequences based on difference sets. A large variety of these sequences can be prepared that are comprised of simple real integer alphabets, whilst imposing few length restrictions. These 'perfect' periodic sequences mimic delta functions through their strong peak, low off-peak, aperiodic auto-correlation. Families of distinct sequences can be produced that exhibit low cross-correlations. These sequences can be used to build discrete impulse-equivalent arrays in higher dimensions. We provide some 2D examples.

Original languageEnglish
Title of host publication2018 International Conference on Digital Image Computing
Subtitle of host publicationTechniques and Applications, DICTA 2018
EditorsManzur Murshed, Manoranjan Paul, Md Asikuzzaman, Mark Pickering, Ambarish Natu, Antonio Robles-Kelly, Shaodi You, Lihong Zheng, Ashfaqur Rahman
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages7
ISBN (Electronic)9781538666029
Publication statusPublished - 16 Jan 2019
EventDigital Image Computing Techniques and Applications 2018 - Canberra, Australia
Duration: 10 Dec 201813 Dec 2018
Conference number: 20th (Proceedings)


ConferenceDigital Image Computing Techniques and Applications 2018
Abbreviated titleDICTA 2018
Internet address


  • coded apertures
  • compressed sensing
  • difference sets
  • ideal autocorrelation sequences
  • sub-sampling masks

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