Number of cosine waves in DCT

1. What is the DCT coefficient?
2. What is discrete cosine transform in DSP?
3. Why is DCT preferred over DFT?
4. How does the discrete cosine transform work?

What is the DCT coefficient?

DCT coefficient (0,0) is the DC coefficient, or average sample value. Since natural images tend to vary only slightly from sample to sample, low frequency coefficients are typically larger values and high frequency coefficients are typically smaller values. The 8×8 DCT is defined in Figure 5.21.

What is discrete cosine transform in DSP?

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression.

Why is DCT preferred over DFT?

> DCT is preferred over DFT in image compression algorithms like JPEG > because DCT is a real transform which results in a single real number per > data point. In contrast, a DFT results in a complex number (real and > imaginary parts) which requires double the memory for storage.

How does the discrete cosine transform work?

The DCT works by separating images into parts of differing frequencies. During a step called quantization, where part of compression actually occurs, the less important frequencies are discarded, hence the use of the term “lossy.