Discrete cosine transform facts for kids

A discrete cosine transform (often called DCT) is a special math process. It helps make things like MP3 music files and JPEG picture files much smaller.

The DCT works by breaking down a sound or a picture into different frequencies. Think of frequencies as the basic building blocks of sounds and images.

This process is called "discrete" because it works with digital information. Digital information is made of separate pieces of data, like samples of a sound or pixels of an image.

How DCT Works with Sounds

For sounds, frequencies are like simple musical tones. Imagine a song. You can make almost any sound by playing many different tones at the same time.

The DCT helps figure out exactly which tones are needed to create a specific sound. The main difference between these tones is their pitch, which is how high or low a sound is.

Our ears are very good at hearing low-pitched sounds. But we are not as good at hearing very high-pitched sounds. When an MP3 player uses DCT to break a sound into tones, it knows this. It doesn't need to keep all the details for the super high tones. This is because most people won't notice if those high tones are slightly changed or removed. This trick helps make the sound file much smaller without losing much quality.

How DCT Works with Pictures

With pictures, frequencies are like different patterns. These patterns can be simple stripes or checkerboard designs. Just like with sound, you can create any picture by combining many different frequency patterns.

Our eyes are also like our ears in some ways. We are not as good at seeing very high frequencies in pictures. High frequencies are things like sharp edges or tiny details. Low frequencies are like smooth colors and gentle changes in shading.

JPEG picture files use this idea. They use DCT to break a picture into its frequency patterns. Then, they can reduce the detail in the high-frequency parts. This makes the picture file smaller. Most people won't notice the missing tiny details, just like with MP3s.

Images for kids

• 

  Nasir Ahmed, the inventor of the discrete cosine transform (DCT), which he first proposed in 1972.

• 

  The four basic stages of computing 3-D DCT-II using VR DIF Algorithm.

• 

  Two-dimensional DCT frequencies from the JPEG DCT

• 

  An example showing eight different filters applied to a test image (top left) by multiplying its DCT spectrum (top right) with each filter.

• 

  Original size, scaled 10x (nearest neighbor), scaled 10x (bilinear).

See also

In Spanish: Transformada de coseno discreta para niños