INTRODUCTION 1.2 ANALOG AND DIGITAL MESSAGES Messages are digital or analog. Digital messages are ordered combinations of finite symbols or codewords. For example, printed English consists of 26 letters, 10 numbers, a space, and several punctuation marks. Thus, a text document written in English is a digital message constructed from the ASCII keyboard of 128 symbols. Human speech is also a digital message, because it is made up from a finite vocabulary in a language.* Music notes are also digital, even though the music sound itself is analog. Similarly, a Morse-coded telegraph message is a digital message constructed from a set of only two symbols-dash and dot. It is therefore a binary message, implying only two symbols. A digital message constructed with M symbols is called an M-ary message. Analog messages, on the other hand, are characterized by data whose values vary over a continuous range and are defined for a continuous range of time. For example, the temperature or the atmospheric pressure of a certain location over time can vary over a continuous range and can assume an (uncountable) infinite number of possible values. A piece of music recorded by a pianist is also an analog signal. Similarly, a particular speech waveform has amplitudes that vary over a continuous range. Over a given time interval, an infinite number of possible different speech waveforms exist, in contrast to only a finite number of possible digital messages.