There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book  by  Elliott  and Rao  is extremely  useful to researchers/engineers who are working  in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

http://ieeexplore.ieee.org/iel5/5/31347/01457444.pdf

Multirate digital signal processing

Provides a tutorial overview of multichannel wireless digital receivers and the relationships between channel bandwidth, channel separation, and channel sample rate. The overview makes liberal use of figures to support the underlying mathematics. A multichannel digital receiver simultaneously down-converts a set of frequency-division-multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver, these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase M-path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple baseband aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator.

Digital receivers and transmitters using polyphase filter banks for wireless communications

Fiber Bragg Grating (FBG) sensors are among the most popular elements for fiber optic sensor networks used for the direct measurement of temperature and strain. Modern FBG interrogation setups measure the FBG spectrum in real-time, and determine the shift of the Bragg wavelength of the FBG in order to estimate the physical parameters. The problem of determining the peak wavelength of the FBG from a spectral measurement limited in resolution and noise, is referred as the peak-tracking problem. In this work, the several peak-tracking approaches are reviewed and classified, outlining their algorithmic implementations: the methods based on direct estimation, interpolation, correlation, resampling, transforms, and optimization are discussed in all their proposed implementations. Then, a simulation based on coupled-mode theory compares the performance of the main peak-tracking methods, in terms of accuracy and signal to noise ratio resilience.

Review and Analysis of Peak Tracking Techniques for Fiber Bragg Grating Sensors.

The latest research works on the synchronization scheme for either continuous transmission mode or burst packet transmission mode for the wireless OFDM communications are overviewed in this paper. The typical algorithms dealing with the symbol timing synchronization, the carrier frequency synchronization as well as the sampling clock synchronization are briefly introduced and analyzed. Three improved methods for the fine symbol timing synchronization in frequency domain are also proposed, with several key issues on the synchronization for the OFDM systems discussed.

On the synchronization techniques for wireless OFDM systems

Due to its attractive properties, generalized frequency division multiplexing (GFDM) is recently being discussed as a candidate waveform for the fifth generation of wireless communication systems (5G). GFDM is introduced as a generalized form of the widely used orthogonal frequency division multiplexing (OFDM) modulation scheme and since it uses only one cyclic prefix (CP) for a group of symbols rather than a CP per symbol, it is more bandwidth efficient than OFDM. In this paper, we propose novel modem structures for GFDM by taking advantage of the particular structure in the modulation matrix. Our proposed transmitter is based on modulation matrix sparsification through application of fast Fourier transform (FFT) to reduce the implementation complexity. A unified demodulator structure for matched filter (MF), zero forcing (ZF), and minimum mean square error (MMSE) receivers is also derived. The proposed demodulation techniques harness the special block circulant property of the matrices involved in the demodulation stage to reduce the computational cost of the system implementation. We have derived the closed forms for the ZF and MMSE receiver filters. Additionally, our algorithms do not incur any performance loss as they maintain the optimal performance. The computational costs of our proposed techniques are analyzed in detail and are compared with the existing solutions that are known to have the lowest complexity. It is shown that through application of our structures a substantial amount of computational complexity reduction can be achieved.

Low-Complexity Modem Design for GFDM

In this paper, we investigate fast-convolution based highly tunable multirate filter bank (FB) configurations. Based on FFT-IFFT pair with overlapped processing, they offer a way to tune the filters' frequency-domain characteristics in a straightforward way. Different subbands are easily configurable for different bandwidths, center frequencies, and output sampling rates, including also partial or full-band nearly perfect-reconstruction systems. Such FBs find various applications, for example, as flexible multichannel channelization filters for software defined radios. They have also the capability to implement simultaneous waveform processing for multiple single-carrier and/or multicarrier transmission channels with nonuniform bandwidths and subchannel spacings. This paper develops an effective model for frequency response analysis and optimization for such filter banks, explores various practical issues of fast-convolution processing and reports the optimized frequency response characteristics versus direct raised cosine based designs. The fast-convolution approach is shown to be a competitive basis for filter bank based multicarrier waveform processing in terms of spectral containment and complexity.

Analysis and Design of Efficient and Flexible Fast-Convolution Based Multirate Filter Banks

The Farrow filter (1988) is a multirate filter structure which offers the option of continuously adjustable resample ratio. This paper presents a derivation of the method proposed by Farrow, and demonstrates the performance and complexity of resampling filters using his technique. The paper also develops some important system options made available to the designer as spin-offs of the derivation.

Performance and design of Farrow filter used for arbitrary resampling

We present a new class of highly effective and low complexity digital filters for processing very wideband signals. Digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval. We will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate. The digital filtering will be shown to include various tasks such as linear/non-linear phase finite impulse response (FIR) filtering, fractional delay filter among others. The proposed technique utilizes the framework of non-maximally decimated filter banks (NMDFBs) with perfect reconstruction (PR) property, which makes the filter bank design simpler and more flexible. Compact representation for the generalized DFT based NMDFBs as well as its efficient polyphase implementation will be provided. The digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks. We will show this embedded intermediate processing elements can achieve spectral shaping/signal manipulation task, which is a generalization of the concept of manipulating a digital filter in the frequency domain. We also analyze both analytically and experimentally, the spectral shaping accuracy based on different design strategies.

Non-Maximally Decimated Analysis/Synthesis Filter Banks: Applications in Wideband Digital Filtering

The authors present a novel design of a wide bandwidth polyphase up-sampling filter bank formed by cascading external shaping filters, arbitrary interpolators and two stages of polyphase channelisation The channeliser synthesises 160 channels with 6-MHz frequency centres and thus spans a two-sided baseband bandwidth of 960 MHz The two stages of channelisation first form super channels from ten sets of 16-channels each in 32-path polyphase channelisers operating at an output sample rate of 192 MHz These ten super channels are, in turn, channelised by a 16-path polyphase channeliser operating at an output sample rate of 1536 MHz The two-stage approach permits the ten sets of first stage super channel channelisers to operate at an easy to implement medium sample rate The complex baseband signal is further up-sampled 1-to-2 and translated to a digital intermediate frequency and pre-compensated for the sin(x)/x distortion of the output digital-to-analogue converter

Fredric J. Harris

Papers

Digital receivers and transmitters using polyphase filter banks for wireless communications

Analysis and Design of Efficient and Flexible Fast-Convolution Based Multirate Filter Banks

Performance and design of Farrow filter used for arbitrary resampling

Non-Maximally Decimated Analysis/Synthesis Filter Banks: Applications in Wideband Digital Filtering

Wideband 160-channel polyphase filter bank cable TV channeliser