[robski]

Mick does the photo of the 64 frequency elements in post 16 help ?

The 8 x 8 is just a manageable block size it could of been 16 x 16 but then it would contained a higher number of frequency components and would make the DCT design very complex. For the same reason the JPEG spec imposes a 14 bit limit on the input channels ( If I recall correctly I don't think it is 12 bit). Hence you can't save as a 16 bit JPEG.

You can get too hung up on the DCT processing. Most of us with an electronics background can understand filters (bandpass, highpass & lowpass) made from coils, resistors and capacitors. Digital filters are something else. Extremely mathematical in their design. In practice their circuits involve shift registers, addition and subtraction units. For example if you shift a set of data 3 places to the right and the add it to the same set of data shifted one place to the left you have performed a mathematical function upon the data. The same principle applies when you sharpen or blur an image in Photoshop. You apply a filter with a mathematical function.

Going off on a similar tangent think about noise reduction. These often use a process called auto-correlation which entails phase shifting the data which smooth out the high frequency pits and bumps. A thing which helped a few things click into place for me in this area was to think about some calculation used in accounting. The one used to average the last 3 years expenditure as time rolls forward to see the general treads rather than focus on a single bad month. If you think about it this is exactly what a lowpass filter is doing. We can change the design by averaging 5 or 7 years instead to get a smoother output.