Low-complexity Multidimensional DCT Approximations

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless $8\times 8\times 8$ approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.Comment: 28 pages, 5 figures, 5 table

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Efficiency in audio processing : filter banks and transcoding

Audio transcoding is the conversion of digital audio from one compressed form A to another compressed form B, where A and B have different compression properties, such as a different bit-rate, sampling frequency or compression method. This is typically achieved by decoding A to an intermediate uncompressed form, and then encoding it to B. A significant portion of the involved computational effort pertains to operating the synthesis filter bank, which is an important processing block in the decoding stage, and the analysis filter bank, which is an important processing block in the encoding stage. This thesis presents methods for efficient implementations of filter banks and audio transcoders, and is separated into two main parts. In the first part, a new class of Frequency Response Masking (FRM) filter banks is introduced. These filter banks are usually characterized by comprising a tree-structured cascade of subfilters, which have small individual filter lengths. Methods of complexity reduction are proposed for the scenarios when the filter banks are operated in single-rate mode, and when they are operated in multirate mode; and for the scenarios when the input signal is real-valued, and when it is complex-valued. An efficient variable bandwidth FRM filter bank is designed by using signed-powers-of-two reduction of its subfilter coefficients. Our design has a complexity an order lower than that of an octave filter bank with the same specifications. In the second part, the audio transcoding process is analyzed. Audio transcoding is modeled as a cascaded quantization process, and the cascaded quantization of an input signal is analyzed under different conditions, for the MPEG 1 Layer 2 and MP3 compression methods. One condition is the input-to-output delay of the transcoder, which is known to have an impact on the audio quality of the transcoded material. Methods to reduce the error in a cascaded quantization process are also proposed. An ultra-fast MP3 transcoder that requires only integer operations is proposed and implemented in software. Our implementation shows an improvement by a factor of 5 to 16 over other best known transcoders in terms of execution speed

Algorithms and Circuits for Analog-Digital Hybrid Multibeam Arrays

Fifth generation (5G) and beyond wireless communication systems will rely heavily on larger antenna arrays combined with beamforming to mitigate the high free-space path-loss that prevails in millimeter-wave (mmW) and above frequencies. Sharp beams that can support wide bandwidths are desired both at the transmitter and the receiver to leverage the glut of bandwidth available at these frequency bands. Further, multiple simultaneous sharp beams are imperative for such systems to exploit mmW/sub-THz wireless channels using multiple reflected paths simultaneously. Therefore, multibeam antenna arrays that can support wider bandwidths are a key enabler for 5G and beyond systems. In general, N-beam systems using N-element antenna arrays will involve circuit complexities of the order of N2. This dissertation investigates new analog, digital and hybrid low complexity multibeam beamforming algorithms and circuits for reducing the associated high size, weight, and power (SWaP) complexities in larger multibeam arrays. The research efforts on the digital beamforming aspect propose the use of a new class of discrete Fourier transform (DFT) approximations for multibeam generation to eliminate the need for digital multipliers in the beamforming circuitry. For this, 8-, 16- and 32-beam multiplierless multibeam algorithms have been proposed for uniform linear array applications. A 2.4 GHz 16-element array receiver setup and a 5.8 GHz 32-element array receiver system which use field programmable gate arrays (FPGAs) as digital backend have been built for real-time experimental verification of the digital multiplierless algorithms. The multiplierless algorithms have been experimentally verified by digitally measuring beams. It has been shown that the measured beams from the multiplierless algorithms are in good agreement with the exact counterpart algorithms. Analog realizations of the proposed approximate DFT transforms have also been investigated leading to low-complex, high bandwidth circuits in CMOS. Further, a novel approach for reducing the circuit complexity of analog true-time delay (TTD) N-beam beamforming networks using N-element arrays has been proposed for wideband squint-free operation. A sparse factorization of the N-beam delay Vandermonde beamforming matrix is used to reduce the total amount of TTD elements that are needed for obtaining N number of beams in a wideband array. The method has been verified using measured responses of CMOS all-pass filters (APFs). The wideband squint-free multibeam algorithm is also used to propose a new low-complexity hybrid beamforming architecture targeting future 5G mmW systems. Apart from that, the dissertation also explores multibeam beamforming architectures for uniform circular arrays (UCAs). An algorithm having N log N circuit complexity for simultaneous generation of N-beams in an N-element UCA is explored and verified