Time-Domain versus Frequency-Domain

Figure 1: Three-dimensional representation of the viewing directions for the time domain and the frequency domain

Figure 1: Three-dimensional representation of the viewing directions for the time domain and the frequency domain

Time-Domain versus Frequency-Domain

For the comparison of the time domain and the frequency domain in signal processing, a three-dimensional model shown in Figure 1 is used. A signal mixture of (here) three sinusoidal frequencies can be viewed in the time domain, which corresponds to the display on an oscilloscope, or in the frequency domain, which corresponds to the display on a spectrum analyzer. In this model, however, all three sinusoidal frequencies are represented on different input channels. If they were only present as a signal mixture on one channel, they would overlap and (here) be represented as a strongly distorted square wave pulse (see: Fourier analysis).

The time domain (TD) is a projection of the model from the direction that the ordinate represents the amplitude or power of the signal. The time is represented in the abscissa. This is a common representation of oscilloscopes or modern network analyzers.

The frequency domain (FD) is a projection of the model from the direction that the ordinate also represents the amplitude or power of the signal. But in the abscissa, the frequency is represented. This representation is supported by spectrum analyzers, filter banks or in the simplest case by frequency-selective voltmeters.

Both viewing directions are only a projection of this three-dimensional model. This applies both to display devices (oscilloscopes or spectrum analyzers) and to signal processing routines since these viewing directions can also be available as an image in a two-dimensional memory structure. Conversion of signals in the time domain to the frequency domain is easily possible with a Fourier transformation. The time domain, on the other hand, is rather a traditional way of observation. In this form, the representation is very informative, because it shows what happens with the signal. Very important for a pulse radar: it shows directly time delays and can, therefore, show the distance for a radar target proportional to the propagation time. This leads directly to the classic radar scope: the A-scope. After this distance measurement, modern radar sets often convert to the frequency range, because then it can be examined whether Doppler frequencies are present and if so, how many. This makes target identification possible. For a linear frequency modulated FMCW radar, distance and, if necessary, radial speed can be determined directly from the value of the frequency of the echo signal. These radars will, therefore, use the frequency range in the displays.