An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also outperform state-of-the-art algorithms in low and high image compression scenarios, exhibiting at the same time a comparable computational complexity.

Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a multitude of compression standards due to its remarkable energy compaction properties. Multiplier-free approximate DCT transforms have been proposed that offer superior compression performance at very low circuit complexity. Such approximations can be realized in digital VLSI hardware using additions and subtractions only, leading to significant reductions in chip area and power consumption compared to conventional DCTs and integer transforms. In this paper, we introduce a novel 8-point DCT approximation that requires only 14 addition operations and no multiplications. The proposed transform possesses low computational complexity and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio. The proposed DCT approximation is a candidate for reconfigurable video standards such as HEVC. The proposed transform and several other DCT approximations are mapped to systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45 nm CMOS technology.

A low-complexity 8-point orthogonal approximate discrete cosine transform (DCT) is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation. Moreover, in several image compression scenarios, the proposed transform could outperform the well-known signed DCT, as well as state-of-the-art algorithms.

The Pettitt test is widely used in climate change and hydrological analyses. However, studies show difficulties of this test in detecting change points, especially in small samples. This study presents a bootstrap application of the Pettitt test, and compares it numerically with the classical Pettitt test by an extensive Monte Carlo simulation. The proposed test outperforms the classical test in all simulated scenarios. An application of the tests is conducted on the historical series of naturalized flows of the Itaipu Hydroelectric Plant in Brazil, for which several studies have shown a change point in the 1970s. When the series is split into shorter sub-series, to simulate actual situations of small samples, the proposed test is more powerful than the classical Pettitt test in detecting the change point. The proposed test can be an important tool for detecting abrupt changes in water availability, in support of hydroclimatological resources decision making.