Maths on need-to-know basis

In a recent survey of the attitude to mathematics of about 800 first-year entrants into engineering departments across 11 UK universities, one question sought to identify the students’ preferred teaching approach: a lot of maths; maths only when unavoidable; absolutely no maths. The responses were respectively 46 per cent, 52 per cent and 1 per cent. When asked the same question, 85 per cent of practising engineers in a group attending a telecommunications short course chose the second option. The fact that the majority of recruits and practitioners in engineering prefer an “engineering first, maths second” approach should influence the way we teach the subject.

Charles Schuler and Mahesh Chugani’s book is the most readable introduction to digital signal processing (DSP) that I have seen. Supported by a CD-Rom, the authors give a non-mathematical and intuitively satisfying treatment of a subject usually wrapped in mathematics. There are nine excellently laid out and brief chapters, each starting with a set of learning objectives and ending with review questions and feedback. Topics covered include analogue-to-digital conversion, correlation and convolution, Fourier series, discrete Fourier transform, windows, digital filters and their implementation and DSP systems.

Anyone who works through this text should gain an unclouded insight into various DSP concepts and a clear appreciation of the parameters involved and their interplay. This type of first encounter with the subject will not only stimulate interest but, crucially, will create knowledge pegs on which to hang a deeper and more mathematically rigorous treatment of DSP.

The books by Chi-Tsong Chen and Michael Roberts give an in-depth treatment of the characterisation of signals and systems and signal processing. Both fully integrate Matlab - a computational software from MathWorks - in their discussion. The chapters are well laid out and include a range of end-of-chapter problems. Topics covered are fairly standard, including signals, systems, Fourier series, Fourier transform, Laplace transform, z Transform, State-Space and the analysis of signals and systems using transform techniques.

Roberts’s book comprehensively covers the above topics using an approach that exhibits the beauty of mathematics. Each chapter begins with a set of goals and concludes with a useful summary of the key points learnt. My only criticism is that its delights of knowledge are not dished out in attractive and bite-sized doses. But those with tenacity will come away with a thorough grounding in the analysis of signals and systems.

Chen emphasises engineering concepts throughout. This allows his target audience of engineering students to appreciate the underlying physical concepts and makes the material attractive and comprehensible.

Ifiok Otung is principal lecturer in communication systems, Glamorgan University.