Malcolm D. Macleod

Use of minimum-adder multiplier blocks in FIR digital filters

The computational complexity of VLSI digital filters using fixed point binary multiplier coefficients is normally dominated by the number of adders used in the implementation of the multipliers. It has been shown that using multiplier blocks to exploit redundancy across the coefficients results in significant reductions in complexity over methods using canonic signed-digit (CSD) representation, which in turn are less complex than standard binary representation. Three new algorithms for the design of multiplier blocks are described: an efficient modification to an existing algorithm, a new algorithm giving better results, and a hybrid of these two which trades off performance against computation time. Significant savings in filter implementation cost over existing techniques result in all three cases. For a given wordlength, it was found that a threshold set size exists above which the multiplier block is extremely likely to be optimal. In this region, design computation time is substantially reduced. >

Variable rate adaptive trellis coded QAM for high bandwidth efficiency applications in Rayleigh fading channels

A high bandwidth efficiency variable rate adaptive channel coding scheme, ATCQAM, is proposed. Known pilot symbols are transmitted periodically to aid demodulation. Past channel states are fed back to the transmitter with delay. Current channel state is then predicted at the transmitter to decide on the appropriate modulation mode for the current symbol. At good channel states, high level modulation is used to boost up the average throughput. At bad channel states, low level modulation is used to increase error protection. By matching the variable modulation level with a variable rate channel coder, the physical bandwidth is maintained constant. Design issues for the ATCQAM are considered. The effects of finite feedback delay, finite interleaving depth and mobile speed are investigated.

Multiplierless FIR filter design algorithms

This letter concerns the design of multiplierless implementations of finite impulse response (FIR) filters to achieve minimum adder cost. Existing approaches include dependence-graph multiplier-block methods and Common Subexpression Elimination (CSE) techniques applied either to the Canonic Signed Digit (CSD) representation of the coefficients or to other Signed Digit (SD) representations. We introduce a new CSE algorithm, which searches a bounded number of Minimal Signed Digit (MSD) representations. The performance of existing algorithms and the new algorithm is compared. It is shown that the relative performance of different algorithms depends on filter length and wordlength and that the new algorithm gives significant improvements in some cases.

Variable-rate adaptive trellis coded QAM for flat-fading channels

A bandwidth-efficient variable-rate adaptive channel coding scheme, ATCQAM, for time-varying flat-fading channels is proposed. In addition to the forward channel, a low-capacity feedback channel is needed to convey channel state information to the transmitter, possibly with delays and noise. A number of transmission modes, with varying throughputs, are incorporated at the transmitter. Appropriate transmission modes are selected based on the feedback channel states. Design issues for the ATCQAM are considered. A closed-loop control scheme to maintain mode synchronization between the transmitter and the receiver is discussed. The effects of feedback delay, a noisy feedback channel, and mobile speed are investigated. Analytical bounds are derived and simulations are performed to verify the results.

Using all signed-digit representations to design single integer multipliers using subexpression elimination

A new algorithm is introduced for design of integer multipliers using subexpression elimination. Hartleys algorithm for subexpression elimination is applied to all possible signed-digit representations of the integer. Results are within 1% of the slow optimal exhaustive searches for 19-bit integers.

Particle filtering applied to musical tempo tracking

This paper explores the use of particle filters for beat tracking in musical audio examples. The aim is to estimate the time-varying tempo process and to find the time locations of beats, as defined by human perception. Two alternative algorithms are presented, one which performs Rao-Blackwellisation to produce an almost deterministic formulation while the second is a formulation which models tempo as a Brownian motion process. The algorithms have been tested on a large and varied database of examples and results are comparable with the current state of the art. The deterministic algorithm gives the better performance of the two algorithms.

Generation of signed-digit representations for integer multiplication

This letter presents an algorithm for generating all of the signed-digit representations of a given integer. There is an infinite number of representations, so the tree algorithm is terminated when a defined number of digits above the minimum possible is reached. It is shown that by having available these other representations, more efficient multiplication circuits can be designed than when using existing algorithms.

Analysis of reassigned spectrograms for musical transcription

The reassignment method for the short-time Fourier transform is proposed as a technique for improving the time and frequency estimates of musical audio data. Based on this representation, four classes of expected objects (sinusoid, unresolved sinusoid, transient and noise) are proposed and explained. Pattern classification methods are then used to extract objects conforming to these classes from individual frames of the reassigned spectrogram, with each frame being examined independently. Results for several simple real-world examples are presented, showing the capability of this method even without the aid of tracking from frame to frame. The main benefits of the proposed reassignment stage are that it yields an improved time-frequency localisation estimate relative to standard methods, and that it produces a measure of the variance of these estimates to be used as an aid in later processing.

Digital filter design using subexpression elimination and all signed-digit representations

We examine the application of Hartleys subexpression elimination algorithm to sets of coefficients that are represented all combinations signed-digits including those that require more digits than CSD. FIR filters using this method can use fewer adders than those designed by the best of existing techniques. However, the search space for practical filters means that exhaustive searching is impractical.

Variable Rate Adaptive Trellis Coded QAM for High Bandwidth Efficiency Applications under Raleigh Fading Channel

A high bandwidth efficiency variable rate adaptive channel coding scheme, ATCQAM, is proposed. Known pilot symbols are transmitted periodically to aid demodulation. Past channel states are fed back to the transmitter with delay. Current channel state is then predicted at the transmitter to decide on the appropriate modulation mode for the current symbol. At good channel states, high level modulation is used to boost up the average throughput. At bad channel states, low level modulation is used to increase error protection. By matching the variable modulation level with a variable rate channel coder, the physical bandwidth is maintained constant. Design issues for the ATCQAM are considered. Practical schemes to maintain transmitter-receiver synchronization, namely the quasi-closed loop control and the closed-loop control, are discussed. The effects of finite feedback delay, finite interleaving depth and mobile speed are investigated.