The last post looked at the basic elements that make up radio communications, so now let’s tackle how some of this can be represented graphically. And just to recap: key concepts are written in bold italic and terms that you’ll often encounter in technical documents are in italic.
Ways of representing signals
Warning: this bit’s going to be a bit mathematical. Feel free to skip it 
There are a number of ways of representing the signals in radio systems. Problems of design or analysis are greatly helped by picking the most convenient representation for the job at hand.
Perhaps the easiest to visualise is the time domain representation. This just describes how some property of the signal, for example, the amplitude or voltage, varies with time. Think of it like an oscilloscope trace.
Signals in the frequency domain can also be represented.
The mathematically inclined will recall the principle of Fourier analysis, where any periodic signal can be decomposed into a set of sinusoidal signals of varying frequency and amplitude. The frequency spectrum of a signal is a plot showing the levels of the different frequency components in the signal. The Fourier Transform and Inverse Fourier Transform allow us to represent a signal in either the time or frequency domain.
The vector representation of a signal is well suited to describing modulation schemes. A common form is the in-phase/quadrature or IQ representation of a signal. Again, for the mathematically inclined, you’ll probably remember pictures like this:
The sinusoidal signal is represented by a vector that rotates (sweeping out a phase angle), and the projection of the vector onto the vertical axis gives the amplitude. The rate of rotation gives the frequency. We can decompose any sinusoidal signal into I and Q components by projecting the signal vector onto the horizontal and vertical axes. If the direction of rotation is reversed this then represents a negative frequency – this is a useful concept. Look at figure 2c and imagine shifting the whole spectrum down in frequency so the carrier is at zero frequency (i.e. baseband). Some of the sidebands will now be at negative frequency. The IQ representation allows negative frequency to be easily dealt with and this representation is very useful when we look at signal constellations in a later post.
Coming next: If you haven’t been put off by the maths (and please don’t be!), then the next post will look at some of the most common elements seen in radio system designs.
How Radios Work: The Series
1. How Radios Work: Basic and key concepts – part A
