Further illustration on the theory behind the Discrete Cosine Transform (DCT) process. Basically the DCT process is measuring the strength of predefined Sine wave patterns in the 8 x 8 pixel block. It is looking for a number of patterns at different frequencies.
Through Fourier's work the concept was developed that said any shape can be broken down into a series of sine wave components of different frequencies and amplitude. The mathematics is very complex but it is easier to understand a visual demonstration of the Fourier principle. Therefore I have managed to find a couple of links to java applets which demonstrate the construction of complex shapes from a series of sine waves of different frequency and strength.
You may need to download a java plug-in to get them to work if your web browser is not already java enabled.
http://www.earlevel.com/Digital%20Au...rmonigraf.html
The first one is very basic. It has 8 sliders which control the amplitude of each frequency. You can see the effect of adjusting the amplitude of each component.
Two buttons are also provided which are programmed to preset the sliders to provide a Sawtooth and Square waveform.
http://www.chem.uoa.gr/applets/Apple..._Fourier2.html
The second link provides some dry theory on the left. On the right is the applet. Press the Clear button to start. Then select one of the eight wave shapes to be demonstrated. The first time you click Add the first harmonic frequency is displayed. Each time you click the add button the next harmonic component is added (shown in the lower window). The more add clicks you make the composite slowly builds up to the required waveform.