The fast type-IV discrete sine transform algorithms for short-length input sequences

In this article, the fast algorithms for the discrete Tchebichef transform (DTT) are proposed for input sequences of lengths in the range from 3 to 8. At present, DTT is widely applied in signal processing, image compression, and video coding. The review of the articles related to fast DTT algorithms has shown that such algorithms are mainly developed for input signal lengths 4 and 8. However, several problems exist for which signal and image processing with different apertures is required. To avoid this shortcoming, the structural approach and a sparse matrix factorization are applied in this paper to develop fast real DTT algorithms for short-length input signals. According to the structural approach, the rows and columns of the transform matrix are rearranged, possibly by changing the signs of some rows or columns. Next, the matched submatrix templates are extracted from the matrix structure and decomposed into a matrix product to construct the factorization of an initial matrix. A sparse matrix factorization assumes that the butterfly architecture can be extracted from the transform matrix. Combining the structural approach with a sparse matrix factorization, we obtained the matrix representation with reduced computational complexity. Based on the obtained matrix representation, the fast algorithms were developed for the real DTT via the data flow graphs. The fast algorithms for integer DTT can be easily obtained using the constructed data flow graphs. To confirm the correctness of the designed algorithms, the MATLAB R2023b software was applied. The constructed factorizations of the real DTT matrices reduce the number of multiplication operations by 78% on average compared to the direct matrix-vector product at signal lengths in the range from 3 to 8. The number of additions decreased by 5% on average within the same signal length range.

Chapter 1 - Discrete Cosine and Sine Transforms

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

This paper presents a new property called the Duality Theorem for the Discrete Sine Transform (DST). Discrete Sine Transform is a finite — length discrete transform which is related to the renowned Discrete Fourier Transform (DFT) and is quite popular in signal processing arena, but has remained in the oblivion from pure mathematicians. Many of the properties of the Discrete Sine Transform are akin to those of the Discrete Fourier Transform and Discrete Cosine Transform, subject to minor differences. A formal derivation of the Duality Theorem corresponding to the Discrete Sine Transform is given which was hitherto not mentioned or derived in the literature. The usage of Duality Theorem helps in finding the discrete time — domain function from the DST frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and hence, saves computation time and cost of implementation to a considerable extent. DST finds applications in Image Processing, Signal Processing applications for Communication Systems, and in the numerical solutions of differential equations as well as partial differential equations of mathematics.

A fast cross spectrum interpolation algorithm of time delay measurement for Passive Satellite Orbit Determination and Tracking is put forward in this paper. The principle, computational complexity and resolution of the fast algorithm are analyzed and an application in a navigation and location system is showed in the ending of the article. It shows that the fast algorithm is efficient and it can meet the requirement of high precision.

Discrete cosine transforms (DCT) are essential tools in numerical analysis and digital signal processing. Processors in digital signal processing often use fixed point arithmetic. In this paper, we consider the numerical stability of fast DCT algorithms in fixed point arithmetic. The fast DCT algorithms are based on known factorizations of the corresponding cosine matrices into products of sparse, orthogonal matrices of simple structure. These algorithms are completely recursive, are easy to implement and use only permutations, scaling, butterfly operations, and plane rotations/rotation-reflections. In comparison with other fast DCT algorithms, these algorithms have low arithmetic costs. Using von Neumann–Goldstine’s model of fixed point arithmetic, we present a detailed roundoff error analysis for fast DCT algorithms in fixed point arithmetic. Numerical tests demonstrate the performance of our results.

In LEO satellite networks, the traditional multicast routing algorithm exist the problem of high computational complexity. In this paper, a fast iterative distributed multicast routing algorithm was developed based on the inherent characteristics of satellite networks which using distributed computing model and significantly reducing the algorithm computational complexity. Simulations show that fast algorithm has low computational complexity, a better average delay performance and overhead compared with the MRA.

With the continuous development of optical fiber sensing technology, the Optical Fiber Pre-Warning System (OFPS) has been widely used in various fields. The OFPS identifies the type of intrusion based on the detected vibration signal to monitor the surrounding environment. Aiming at the real-time requirements of OFPS, this paper presents a fast algorithm to accelerate the detection and recognition processing of optical fiber intrusion signals. The algorithm is implemented in an embedded system that is composed of a digital signal processor (DSP). The processing flow is divided into two parts. First, the dislocation processing method is adopted for the sum processing of original signals, which effectively improves the real-time performance. The filtered signals are divided into two parts and are parallel processed by two DSP boards to save time. Then, the data is input into the identification module for feature extraction and classification. Experiments show that the algorithm can effectively detect and identify the optical fiber intrusion signals. At the same time, it accelerates the processing speed and meets the real-time requirements of OFPS for detection and identification.

Of the acoustical source localization algorithms that have been proposedin the literature, mostcan be dividedinto two separate groups. While some algorithmsare robust, they are computationally complex. Conversely, the fast algorithms cannot localize robustly in real world scenarios. Recently several new algorithms have been proposed that are robust and fairly fast, including Hierarchical Localization and Hybrid Localization. A method for optimal placement of candidate locations will be presented, which reduces computational complexity of Hierarchical Localization. The performance of Hierarchical Localization and Hybrid Localization will be compared in both simulated and real scenarios. It will be shown that Hybrid Localization is more robust than Hierarchical Localization and also computationally faster.

H.264 video coding standard gains significant improvement in compression efficiency. However, the computational complexity also considerably increases. Many fast algorithms are introduced to speed up the encoding. Distinguishing from pervious multi-frame based fast motion estimation algorithms which only exploit temporal correlation, a novel algorithm both employing temporal and spatial correlations is proposed in this paper, which has much better prediction accuracy. To further speed up the encoding process, an adaptive mode reduction scheme which will discard small probability modes is also proposed. Combining the novel fast multi-frame based motion estimation algorithm and the adaptive mode reduction scheme, experimental results show that the proposed algorithms improve the encoding speed by an average of 9 times faster than fast full search and about 2.5 times faster than reference method which only employs temporal correlation, PSNR dropping and bitrate increasing are negligible.

In the recent times, Visible Light Communication (VLC) has evolved as a new communication standard due to its stunning notability to render ubiquitous connectivity by emerging as a prominent revolutionary to radio frequency (RF) based wireless communications. However, an orthogonal frequency division multiplexing (OFDM) based VLC system is susceptible to timing errors. Therefore, this work addresses the synchronization aspects in asymmetrically clipped optical OFDM (ACO-OFDM) system which is exploiting real trigonometric transform like discrete sine transform (DST). The striking notability is that without the necessity of Hermitian Symmetry criteria, this optical OFDM system takes the advantages of real signal processing transformation technique like DST. Thus, this technique reinforces the transmission of double the data symbols in comparison to conventional optical OFDM system which is based on standard Fourier signal processing. Besides, this work derives the elaborate mathematical expressions illustrating the deleterious effects of unreliable timing errors in DST-based ACO-OFDM system. In addition, this paper interprets as well as compares the performance of timing synchronization algorithms exploiting the periodicity property of the optical OFDM symbol with the training symbol based STO estimation algorithm in DST-based ACO-OFDM system. Moreover, this work validates the derived Cramer Rao Lower Bound (CRLB) and the simulated results infer that derived CRLB pertaining to the timing errors contributes the minimum mean square error (MSE) when compared with other STO estimation algorithms.

Intraprediction has been significantly improved in high efficiency video coding over H.264/AVC with quad-tree-based coding unit (CU) structure from size 64×64 to 8×8 and more prediction modes. However, these techniques cause a dramatic increase in computational complexity. An intracoding algorithm is proposed that consists of perceptual fast CU size decision algorithm and fast intraprediction mode decision algorithm. First, based on the visual saliency detection, an adaptive and fast CU size decision method is proposed to alleviate intraencoding complexity. Furthermore, a fast intraprediction mode decision algorithm with step halving rough mode decision method and early modes pruning algorithm is presented to selectively check the potential modes and effectively reduce the complexity of computation. Experimental results show that our proposed fast method reduces the computational complexity of the current HM to about 57% in encoding time with only 0.37% increases in BD rate. Meanwhile, the proposed fast algorithm has reasonable peak signal-to-noise ratio losses and nearly the same subjective perceptual quality.

An adaptive filtering algorithm based on an Euclidean direction search (EDS) method is presented for image restoration. It is a fast algorithm and has a computational complexity of O(N) for least squares optimization. Computer simulations illustrate that this algorithm is very effective in image restoration. The figures for signal-to-noise ratio improvement (SNRI) produced by this algorithm are comparable to those obtained by using the recently reported sample-based conjugate gradient (SCG) algorithm, which has a computational complexity of O(N/sup 2/). This algorithm can also be extended to other applications in adaptive signal processing.

Anytime signal processing algorithms are to improve the overall performance of larger scale embedded digital signal processing (DSP) systems. In such systems there are cases where due to abrupt changes within the environment and/or the processing system temporal shortage of computational power and/or loss of some data may occur. It is an obvious requirement that even in such situations the actual processing should be continued to insure appropriate performance. This means that signal processing of somewhat simpler complexity should provide outputs of acceptable quality to continue the operation of the complete embedded system. The accuracy of the processing will be temporarily lower but possibly still enough to produce data for qualitative evaluations and supporting decisions. In this paper a new fast anytime fuzzy Fourier transformation algorithm is introduced. The presented method reduces the delay problem caused by the block-oriented fast algorithms and at the same time keeps the computational complexity on relatively low level. It makes possible the availability of good quality partial results or estimates before the samples of the period arrive, which can be advantageous in case of abrupt reaction need, long or possibly infinite input data sequences.

A fast algorithm for discrete sine transform (DST) is proposed. Through derivation the traditional DST is transformed into the computation of a first-order moment, which can be implemented by a simple parallel structure without multiplications. The comparison with some existing methods on the computation and the hardware complexity shows the advantage of our method under certain conditions. The approach is also applicable to other discrete sine transforms.