3.1 Signals
No useful information can communicated by anything that remains perfectly constant. Think about it. If a communications system is using electricity and cables as its medium, the the transmitter must vary the current flowing in the cables so that this variation can be detected by the receiver. Deciding exactly which voltages and currents to use to represent different digits is part of the design process carried out by electronic engineers. If the communication system uses light (with, say, optical fibres) then the transmitter must vary the intensity or colour of the light to generate a useful signal.
3.2 Waveforms
A waveform is a graph of the variation of something over time. The `something' may be voltage, current, light intensity, or anything else. The figure below shows the waveform that might be measured at the output of the transmitter in a digital system. In this example, if 1 volt represents a binary digit `one' and 0 volts represents a `zero', then the binary data being communicated is `10010111...'
Note that both the axes of the graph have scales with units. The time axis in this case is labelled in milliseconds (a millisecond is a 0.001 seconds). So it can be seen that each digit requires 1 millisecond to transmit.
This waveform is non-repetitive, that is, we cannot assume that the same signal will be repeated over and over again. If a waveform is repetitive, that is, repeats continuously, then its important characteristic is its frequency.
Figure 1: A typical digital waveform
3.3 Frequency
The frequency of a waveform or signal is the rate at which it repeats. Frequency is measured in cycles per second (cps) or, more often, Hertz (Hz). These two units are equivalent; 100 cps = 100 Hz. 1 Hz is a rather low frequency for communications work. Normally communications engineers work with frequencies of megahertz (MHz). 1 MHz = 1 million Hz.
Strictly speaking, only repetitive waveforms have a frequency. And as most real information is not repetitive, the signals carrying that information do not really have a frequency. However, it is quite common to talk about the frequency of a signal. When we say that the signal being transmitted has a `frequency of 1000 Hz', we really mean that it looks a bit like a repetitive signal with this frequency, or that its average frequency is 1000 Hz.
Waveforms encountered in communications system typically have frequencies from a few hundred Hz (e.g., the electrical signal coming from the microphone of a telephone handset) up to a few thousand megahertz (e.g, the signals received from communications satellites).
3.4 Wavelength
Communications engineers who specialize in radio and satellite systems mormally express frequency in terms of wavelength. If a signal is travelling through the air, or through space, its variation over time gives rise to a variation with distance from the transmitter. This can be seen if you tie a piece of rope to a doorhandle and wave the other end up and down. The variation in position over time translates to a pattern along the length of the rope.
If we know how fast a signal is travelling, we can always convert the frequency to a wavelength or vice versa. Moreover, as most important communications systems send information at approximately the speed of light, the conversion can normally be carried out the same way. As a rough guide, a frequency of 1 MHz corresponds to a wavelength of 300 metres. There is no particular advantage to expressing speed of variation of a signal in wavelength compared to frequency. Ideally you should be familiar with both methods.
Light also has a wavelength (and a frequency), but it is too short to measure with electrical apparatus. The wavelength of a light beam is manifested by its colour. Blue light has a shorter wavelength (higher frequency) than red light. Some light sources can have their wavelengths altered by an electrical signal. This makes them very useful in communications systems.
3.5 Frequency components
Two signals may have the same fundamental frequency, but still be different. This is shown in the figure below. A `sawtooth' waveform can be seen to be comprised of a number of smoothly-varying signals. These smoothly-varying signals are technically sinewaves;the shape has important mathematical properties that I won't go into here. The sinewave of lowest freqency is called the fundamental; you should be able to see that this has the frequency as the basic repetition rate of the sawtooth. 
Figure 2: A `sawtooth' signal, and its representation as a series of sinewaves
The understanding of frequency components is important in the study of sampling, that is, conversion of an analogue signal to a digital one.
3.6 Frequency series and spectrum
If you understand the idea of frequency components, the concept of a frequency series is not complicated. It is simply a graph of amplitude against frequency, showing the frequency components. The figure below shown the frequency series that coresponds to the sawtooth waveform. There is a peak in the graph at each of the freqencies of the frequency components of the signal. The sawtooth has components at 1Hz, 2Hz, etc, each of which is smaller than the next. A frequency series is simply a convenient way of showing the frequency components of a signal.
To a mathemetician or physicist, there is an important distinction between a frequency series and a frequency spectrum. Communications engineers tend to use the term `spectrum' for both. This is sloppy, but the mathematical distinction is a subtle one and beyond the scope of this document.
Figure 3: Frequency series for the sawtooth waveform described above
©1994-2006 Kevin Boone, all rights reserved