In this article, it is shown that Unified Complex Hadamard Transform (UCHT) can be derived from Walsh functions and through direct matrix operation. Unique properties of UCHT are analyzed. Recursive relations through Kronecker product can be applied to the basic matrices to obtain higher dimensions. These relations are the basis for the flow diagram of a constant-geometry iterative VLSI hardware architecture. New Normalized Complex Hadamard Transform (NCHT) matrices are introduced which are another class of complex Hadamard matrices. Relations of UCHT and NCHT with other discrete transforms are discussed.

The UCHT (Unified Complex Hadamard Transform) has been proposed as a new family of spreading sequences for DS-SSMA systems recently. In this Letter, the periodic autocorrelation (PAC) properties of the Unified Complex Hadamard Transform (UCHT) sequences are analyzed. Upper bounds for the out-of-phase PAC are derived for two groups of the UCHT sequences, namely the HSP-UCHT and the NHSP-UCHT sequences (the later is a more general representation of the well-known Walsh-Hadamard (WH) sequences). A comparison of the two bounds is performed. It turns out that the HSP-UCHT sequences have a lower upper bound for the out-of-phase PAC. This makes the HSP-UCHT sequences more effective than the WH sequences in combating multipath effect for DS-SSMA systems.

High dynamic range (HDR) images contain more details of the scene as compared to commonly used low dynamic range (LDR) images. The additional information in the HDR images is important for applications such as high-quality graphics rendering, sensing, scene analysis, and surveillance etc. Moreover, HDR images would provide better visualization experience on HDR displays, which might become more common in near future. Therefore, it is important to encode the entire dynamic range of the HDR images. In this paper, a new lossless, four-channel, eight bits per channel, format for encoding floating-point HDR images is proposed. The format is similar to the well-known RGBE format but constructs the E channel differently for better accuracy. Experimental results show that our technique could reduce the rounding error of the RGBE by more than 88%. In addition, there was a reduction of 44.3% in average error for all 33 images in the database used for this study.

In this paper, comparison of various orthogonal transforms in Wiener filtering is discussed. The study involves the family of discrete orthogonal transforms called Complex Hadamard Transform, which has been recently introduced by the same authors. Basic definitions, properties and transformation kernel of Complex Hadamard Transform are also shown.