Signal Processing based on Stable radix-2 DCT Algorithms having Orthogonal Factors
This work offers numerically stable DCT algorithms for signal processing applications, but the improvements are incremental over existing recursive DCT methods.
The paper presents stable, radix-2, completely recursive DCT algorithms with orthogonal factors and provides error bounds. Image compression results show 93.75% coefficient absence for 512x512 images with various block sizes.
This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having sparse and orthogonal factors are addressed. Image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size $512 \times 512$ pixels with transfer block sizes $8 \times 8$, $16 \times 16$, and $32 \times 32$ with $93.75\%$ absence of coefficients in each transfer block. Finally signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors.