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On Lifting-Based Fixed-Point Complex Multiplications and Rotations
Linköping University, Department of Electrical Engineering, Computer Engineering.ORCID iD: 0000-0003-3470-3911
2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Lifting-based complex multiplications and rotations are integer invertible, i.e., an integer input value is mapped to the same integer output value when rotating forward and backward. This is an important aspect for lossless transform-based source coding, but since the structure only require three real-valued multiplications and three real-valued additions it is also a potentially attractive way to perform complex multiplications when the coefficient has unity magnitude. In this work, we consider two aspects of these structures. First, we show that both the magnitude and angular error is dependent on the angle of input value and derive both exact and approximated expressions for these. Second, we discuss how to design such structures without the typical separation into three subsequent matrix multiplications. It is shown that the proposed design method allows many more values which are integer invertible, but can not be separated into three subsequent matrix multiplications with fixed-point values. The results show good correspondence between the error approximations and the actual error as well as a significantly increased design space.

Place, publisher, year, edition, pages
2017.
Keyword [en]
Rotation, complex multiplication, error analysis, fixed-point representation
National Category
Computer Systems Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-139336OAI: oai:DiVA.org:liu-139336DiVA: diva2:1121297
Conference
IEEE Symposium on Computer Arithmetic
Available from: 2017-07-10 Created: 2017-07-10 Last updated: 2017-07-10

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
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Language
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
  • html
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  • asciidoc
  • rtf