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

Spread-spectrum (SS)-based pulsewidth modulation (PWM) techniques play an important role when tackling the electromagnetic interference (EMI) problem in the switch-mode power supply (SMPS) domain. They achieve the best EMI noise reduction and emerge as a promising and very effective solution to comply with electromagnetic standards. The current work provides an insight into the SS techniques: its history, its types, and mainly its ability to mitigate the EMI problem in the SMPS domain. Moreover, it gives a short review of the different SS-based PWM techniques going from the most basic and simple, i.e., the periodic modulation, to the most developed and complex, i.e., the random and chaotic modulations. Besides, a short review of the different implementation methods was addressed and they were categorized into analog and digital implementation techniques where its pros and cons were provided. Finally, a new fast digital implementation method based on a dsPIC33F microcontroller is presented. Its effectiveness was proved and its advantages over the reviewed implementation techniques were recognized. It reached a 20 dBuV EMI level reduction when the digital chaotic and periodic profiles were embedded into a boost converter prototype.

A Review of Spread-Spectrum-Based PWM Techniques—A Novel Fast Digital Implementation

A digital Class-D amplifier comprises a pulsewidth modulator (PWM) and an output stage. In this paper, we simplify the time-domain expression for the algorithmic PWM linear interpolation (LI) sampling process and analytically derive its double Fourier series expression. By means of our derivation, we show that the nonlinearities of the LI process are very low, especially given its modest computation complexity and low sampling frequency. In particular, the total-harmonic distortion (THD) /spl ap/0.02% and foldback distortion is -98.4 dB (averaged from modulation indexes M=0.1 to 0.9) for the 4-kHz voiceband bandwidth @1-kHz input, 48-kHz sampling. We also describe a simple hardware for realizing the LI process. We propose a frequency doubler (with small overheads) for the pulse generator for the PWM, thereby reducing the counter clock rate by 2, leading to a substantial /spl sim/47% power dissipation reduction for the Class-D amplifier. By means of computer simulations and on the basis of experimental measurements, we verify our double Fourier series derivation and show the attractive attributes of a Class-D amplifier embodying our simplified LI sampling expression and reduced clock rate pulse generator. We show that our Class-D amplifier design is micropower (/spl sim/60 /spl mu/W @1.1 V and 48-kHz sampling rate, and THD /spl ap/0.03%) and is suitable for practical power-critical portable audio devices, including digital hearing aids.

/pdf/a-micropower-low-distortion-digital-class-d-amplifier-based-3o0pr8zj6u.pdf

A micropower low-distortion digital class-D amplifier based on an algorithmic pulsewidth modulator

Two 128-point 16-bit radix-2 FFT/IFFT processors based on synchronous-logic (sync) and asynchronous-logic (async) for low voltage (1.1-1.4 V) energy-critical low-speed hearing aids are described. The two processors herein are designed with the same function and similar architecture, and the emphasis is energy efficacy. The async approach, on average, features ~37% lower energy per FFT/IFFT computation than the sync approach but with ~10% larger IC area penalty and an inconsequential 1.4 times worse delay; the async design can be designed to be 0.24 times faster and with largely the same energy dissipation if the matched delay elements and the latch controllers therein are better optimized. In this low-speed application, the lower energy feature of the async design is not attributed to the absence of the clock infrastructure but instead due to the adoption of established and proposed async circuit designs, resulting in reduced redundant operations and reduced spurious/glitch switching, and to the use of latches. The prototype async FFT/IFFT processor (in a 0.35-mum CMOS process) can be operated at 1.0 V and dissipates 93 nJ.

Energy-Efficient Synchronous-Logic and Asynchronous-Logic FFT/IFFT Processors

The total harmonic distortion (THD) and the power supply noise, qualified by the power supply rejection ratio (PSRR) and by the power supply induced intermodulation distortion (PS-IMD), are recognized to be potential drawbacks of class D amplifiers. In this paper, analytical expressions for the THD, PSRR, and PS-IMD of the bang-bang control class D amplifier (bang-bang amp) are derived; the bang-bang amp is arguably the most power-efficient class D amp for low-voltage power-critical applications including hearing aids. Based on the derived expressions, the effects of important parameters on the THD, PSRR, and PS-IMD are investigated, providing good insight to the design of the bang-bang amp to meet given design specifications. The analytical analyses are verified by comparing them against HSPICE simulations and hardware measurements. The bang-bang amp is also compared against the prevalent pulsewidth modulation class D amp, and in most cases, the former is shown to possess superior parameters, including lower power dissipation and hardware advantages for low-voltage power-critical applications.

Bang-Bang Control Class D Amplifiers: Total Harmonic Distortion and Supply Noise

We present a novel randomized wrapped-around pulse position modulation (RWAPPM) scheme for digital modulators of dc-dc converters. Unlike the reported modulation schemes that require a varying switching period (thereby resulting in high attenuation or complete elimination of discrete harmonics), the proposed RWAPPM conversely requires only a constant switching period (thereby advantageous in terms of easy realization in hardware), and yet, its discrete harmonics are negligible. We derive an expression for the spectrum of the RWAPPM scheme to analytically obtain the peak spectral power and ripple noise voltage of RWAPPM. This expression further provides insight to the parameters that influence the RWAPPM spectrum. We benchmark the RWAPPM scheme against the ubiquitous conventional pulsewidth modulation scheme and six reported (randomized and frequency modulation) schemes. The RWAPPM scheme features negligible discrete harmonics [≤ -158 dB relative to full scale (dBFS)], and among the modulation schemes, it features the lowest peak spectral power at -26.6 dBFS (before low-pass filtering) and relatively low ripple noise at 2 mVrms (after low-pass filtering) for a 3.6-2.5-V conversion and an effective switching frequency of 120 kHz. We verify the derived expression and attributes of the RWAPPM spectrum by computer simulations and on the basis of experimental measurements on a dc-dc converter.

A Randomized Wrapped-Around Pulse Position Modulation Scheme for DC–DC Converters

We present a micropower digital modulator for class-D amplifiers for power-critical digital hearing aids. The modulator design embodies a proposed Lagrange interpolation (a combined first- and second-order Lagrange) algorithmic pulsewidth modulation (PWM) and a third-order DeltaSigma noise shaper. By means of double-Fourier-series analysis, we analyze and determine the harmonic nonlinearities of the proposed algorithmic PWM. At 48-kHz sampling, 96-kHz PWM output, 997-Hz input, and input modulation index=0.9, the modulator circuit achieves a total harmonic distortion+noise n(THD+N) of - 74ndB (0.02%) over an 8-kHz voice bandwidth-a 12-dB THD+N improvement over a reported design and yet dissipates only ~ 50% of the power. The proposed modulator dissipates the lowest power dissipation of all modulators compared, and by means of a proposed figure of merit, the proposed modulator exhibits very competitive performance. The modulator IC is fabricated in a 0.35-mum digital CMOS process with a core area of 0.46 mm2.

/pdf/a-low-voltage-micropower-digital-class-d-amplifier-modulator-4iyc7mp33o.pdf

A Low-Voltage Micropower Digital Class-D Amplifier Modulator for Hearing Aids

We propose a novel low-harmonics low-noise modulation scheme for switched-mode dc–dc converters. The proposed scheme is a hybrid of a randomized modulation scheme, namely, the randomized wrapped-around pulse position modulation scheme (RWAPPM), and a noise-shaper. The RWAPPM mitigates the switching-frequency harmonics in the input current, whereas the noise-shaper mitigates the low-frequency noise therein. We derive an analytical expression for the input current spectrum of the hybrid scheme. We benchmark the hybrid scheme against the conventional pulse width modulation scheme (PWM) and the RWAPPM without the noise-shaper. At 0.5 duty cycle, 3.3-V input voltage, 100-kHz average switching frequency, and with the second-order noise-shaper, the peak spectral power in the input current spectrum of the hybrid scheme is 18.1 dB lower than the PWM. Other randomized and spread-spectrum modulation schemes, in general, have undesirably higher input noise current than that of the PWM. However, the input noise current of the proposed hybrid scheme, obtained at ~73-mA rms (integrated over a 200-kHz bandwidth without an input filter), is comparable with that of the PWM, and is lower by ~16-mA rms compared with that of the RWAPPM without the noise-shaper. We also benchmark the hybrid scheme against other well known randomized and spread-spectrum modulation schemes. We further propose a novel pulse generator structure that embodies the hybrid scheme. We realize a dc–dc converter employing the pulse generator, and measure the converter to verify the derived expression and the characteristics of the hybrid scheme. We also measure the output voltage spectrum, the transient-response, and the operating range of the converter.

A Noise-Shaped Randomized Modulation for Switched-Mode DC-DC Converters

We propose a novel Direct Interpolation (DI) sampling process and novel hybrid pulse generator for a Pulse Width Modulator (PWM) for a digital Class D amplifier. The DI sampling process features the lowest harmonic distortion compared to other algorithmic sampling processes. The computation for the DI process is simple, leading to small IC area and very low power dissipation (7 /spl mu/W@1.1 V). We analytically derive the double Fourier expression for the DI process and show that the THD is very low (<0.03%). The novel hybrid pulse generator embodies a counter, noise shaper, and novel 1-bit frequency doubler. The complete PWM features a simple circuit implementation (small IC area), micropower low voltage operation (/spl sim/60 /spl mu/W@1.1 V), low sampling rate (48 kHz) and low harmonic distortion (/spl sim/0.03%).

Victor Adrian

Papers

A micropower low-distortion digital class-D amplifier based on an algorithmic pulsewidth modulator

A Randomized Wrapped-Around Pulse Position Modulation Scheme for DC–DC Converters

A Low-Voltage Micropower Digital Class-D Amplifier Modulator for Hearing Aids

A Noise-Shaped Randomized Modulation for Switched-Mode DC-DC Converters

A novel sampling process and pulse generator for a low distortion digital pulse-width modulator for digital class D amplifiers