The most common representation of signals and waveforms is in the time domain. However, most signal analysis techniques work only in the frequency domain. The concept of the frequency domain representation of a signal is quite difficult to understand when one is first introduced to it. This tutorial attempts to explain the frequency domain representation of signals. You should refer to this tutorial whenever you become confused about this very important form of signal representation.
The frequency domain is simply another way of representing a signal. For example, consider a simple sinusoid.
The time - amplitude axes on which the sinusoid is shown define the time plane. If an extra axis is added to represent frequency, then the sinusoid would be as illustrated below.
The frequency - amplitude axes define the frequency plane in a manner similar to the way the time plane is defined by the time - amplitude axes. This frequency plane is what is represented when the spectrum of a signal is shown.
The frequency plane is orthogonal to the time plane, and intersects with it on a line which is the amplitude axis.
Note that the time signal can be considered to be the projection if the sinusoid onto the time plane (time - amplitude axes). The actual sinusoid can be considered to be as existing some distance along the frequency axis away from the time plane. This distance along the frequency axis is the frequency of the sinusoid, equal to the inverse of the period of the sinusoid.
The waveform also has a projection onto the frequency plane. If you imagine yourself standing on the frequency axis, looking toward the sinusoid, you would see the sinusoid as simply a line. This line will have a height equal to the amplitude of the sinusoid. So, the projection of the sinusoid onto the frequency plane is simply a line equal to the amplitude of the sinusoid.
These two projections mean that the sinusoid appears as a sinusoid in the time plane (time - amplitude axes), and as a line in the frequency plane (frequency - amplitude axes) going up from the frequency of the sinusoid to a height equal to the amplitude of the sinusoid.
It should be noted very carefully that all the information about the sinusoid (frequency, amplitude and phase) is represented in the time plane projection, but all phase information is lost in the projection onto the frequency plane. If the full signal is to be reconstructed from the frequency representation then an additional graph called the phase diagram is needed. The phase diagram is simply a graph of the phase versus frequency, similar to the amplitude versus frequency graph obtained from the frequency plane.
Although this tutorial has only examined a sinusiodal waveform, it is relevant to all waveforms because any non-sinusoidal waveform can be expressed as the sum of various sinusoidal components. This is achieved by Fourier series expansion (see Tutorial 1 ).
