Algorithmic engineering as a teaching aid for DSP

The concept of algorithmic engineering was introduced by McWhirter (see IEE Proc.-E, vol.139, no.3, June 1992) in the context of adaptive signal processing. In effect, it constitutes a simple but rigorous diagrammatic approach to the design of parallel algorithms and architectures for digital signal processing. For the purposes of this design methodology, a parallel algorithm is represented in terms of its basic signal flow graph (SFG). In the context of teaching DSP, this could be of particular advantage. In the article, the potential use of algorithmic engineering as a design and teaching aid is illustrated by means of two particularly relevant examples. The first relates to the FFT. The second concerns the least squares lattice algorithm for linear prediction and adaptive filtering. It is shown how each can be derived, and hence taught, by starting with the SIG for a more basic algorithm (the DFT and recursive least squares algorithms respectively) and then applying a sequence of simple diagrammatic transformations. The least squares lattice derivation starts with the SFG for a multichannel least squares adaptive filter based on QR decomposition