Fourier Transform on measuring temperature

The Fourier transform converts a set of time domain data vectors into a set of frequency (or per time) domain vectors.

To know about changes in soil temperature, we can measure the temperature of soil accordingly at different time of the day, every day for a year. We would then have a list of real numbers representing the soil temperatures.

By plotting these readings on a line graph with the vertical y axis labelled as temperature and the horizontal x axis labelled time, we get a so called “time domain” graph. The graph that we created is then the sum of two  sinusoids or sine waves. The first sinusoid is with a frequency of one day as the temperature varies between day and night. The other sinusoid is with a frequency of one year as the temperature varies with the seasons.

The Fourier Transform provides a means of manipulating or transforming this raw data into an alternative set of data, the magnitude of which can be plotted on a graph with differently labelled axis. Disregarding the y axis label for now, the x axis would be labelled ‘frequency’. This is in the frequency domain graph.

This second graph looks very different than the first because it will consist of two vertical lines rising from the frequency axis, one at a frequency (or period) of one day, the other at a frequency of one year. Thus by using Fourier Transform on the raw data we have, we then extracted the most interesting facts from it – days are warmer than nights and summer is warmer than winter.