We start by defining some important terms in digital filter theory.

A sampled data filter is an algorithm for converting a sequence of continuous amplitude analogue samples into another (analogue) sequence. The filter output sequence could then be lowpass filtered to recover a continuous time or analogue signal, and the overall filtering effect will be similar to that of conventional analogue filtering in the sense that we can associate a frequency response with the sampled data filter. In Section 4.1 we develop a formal discrete time linear filter theory based upon the concept of sampled data filtering.

Usually the signal is both sampled and quantized and the filter input is actually a sequence of n-bit words. The filter is then referred to as a digital filter, and it could be implemented in digital hardware or as a software routine on a DSP chip. For generality, the basic digital filter theory developed in Section 4.1 neglects quantization effects and treats the digital filter as a sampled data filter.

A practical example of a true sampled data filter is the CCD transversal filter used for ghost reduction in television receivers. Here, CCD rather than digital technology is sometimes preferred because it offers a long delay time in a small chip area with low power consumption. Examples of digital filters abound. Adaptive digital filtering can be used to reduce the noise level in aircraft passenger compartments (using adaptive acoustic noise cancellation), and adaptive transversal digital filters can be used for equalization of telephone lines.

Readership

This book has been written for students who are in the middle or final years of a degree in electronic or communication engineering and who are following a course in signal coding and signal processing techniques. It should also be helpful to engineers and managers in industry who need an introductory or refresher course in the field.

About the book

Many textbooks are devoted to either signal coding, e.g. error control, or to signal processing, e.g. digital filters, simply because there is great breadth and depth in each area. On the other hand, practical systems invariably employ a combination of these two fields and a knowledge of both is often required. For example, a knowledge of digital filtering, fast Fourier transforms (FFTs) and forward error control would often be required when designing a satellite data modem. Similarly, a knowledge of discrete transforms is fundamental to the understanding of some video compression schemes (transform coding), and basic digital filter theory is required for some speech codecs. Also, many undergraduate courses give an introduction to both fields in the middle and final years of a degree.

The philosophy behind this book is therefore to provide a single text which introduces the major topics in signal coding and processing, and to illustrate how these two areas interact in practical systems. The book is a blend of theory and modern practice and is the result of some 12 years lecturing and research experience in these two fields.

The broad objective of channel coding is to ‘match’ the source data to the transmission channel, and the coding techniques involved generally fall under the heading of either error control coding (ECC) or transmission coding. Scrambling techniques are often used to improve synchronization and can also be regarded as a form of channel coding.

Overview of ECC

Fig. 3.1 gives an overview of ECC techniques. Two main classes of error control are used to achieve an acceptable error rate at the receiver, namely, automatic repeat request (ARQ) and FEC. ARQ uses an error detecting code together with a feedback channel to initiate retransmission of any block received in error. It can be used where time delay is permissible, e.g. in data transmission. In contrast, FEC controls the received error rate via forward transmission only. In its simplest form, FEC amounts to error concealment, Fig. 3.2. Here, upon detection of a parity error the receiver could repeat the last most suitable word. Alternatively, after detection an isolated erroneous sample could be replaced by a linear interpolation between its two neighbours. The latter type of concealment is used on compact disc systems when an error correction code is overloaded, thereby avoiding sharp audio ‘clicks’. Concealment techniques are simple to implement, but have restricted applications. For example, they are not applicable to computer systems, or to systems where sample-to-sample correlation has already been exploited, e.g. DPCM systems.

This chapter examines theoretical and practical aspects of pulse code modulation (PCM) because of its direct relevance to the coding techniques presented in Chapters 2 and 3.

We start by comparing PCM with Shannon's ideal coding concept and by highlighting its noise immunity compared to uncoded systems. The chapter then examines the two fundamental aspects of PCM (sampling and quantizing) from theoretical and practical standpoints, and illustrates how sampling rates and quantizing noise can be ‘adjusted’ in order to convert efficiently analogue signals to PCM or vice-versa. Once in PCM form, a signal is usually processed by some source coding technique in order to satisfy a specific bit rate, and PCM network standards are outlined in Section 1.6.2. The chapter concludes by introducing the idea of channel coding, which is essentially a mechanism for matching the processed PCM signal to the transmission channel.

The ideal coding concept

Consider the receiver in Fig. 1.1 (essentially a demodulator or decoder) where Si and Ni are the average signal and noise powers for the input, So and No are the average signal and noise powers for the output, BT is the transmission bandwidth and Bm is the message bandwidth. In general (but not always) a practical receiver improves the signal-to-noise ratio (SNR) in exchange for signal bandwidth, so that by choosing a modulation or coding scheme such that BT ≫ Bm it should be possible for the receiver to deliver a high-quality signal despite a low Si/Ni ratio.