Fixed-point Processor Research Articles

Quantization effects in the complex LMS adaptive algorithm: Linearization using dither-theory

This paper describes the use of dither to linearize the gradient quantizer in a digitally implemented LMS adaptive algorithm. When the LMS algorithm is implemented in a fixed-point digital processor, a choice must be made between rounding the gradient estimate before addition to the contents of the weight accumulator, or rounding the weight at the accumulator output and operating a double-precision accumulator. Because of hardware constraints, the former approach is often elected. However, when the weight accumulator input is quantized, care must be exercised to prevent the algorithm from stalling. To overcome this difficulty, a sequence of random vectors, called "dither," is used to "linearize" the gradient quantizer. A difference equation for the weight covariance matrix is derived, and a solution for transient mean-square error is obtained that includes both the effects of dither and quantization noise.

The ADF, an experimental self-adaptive digital filter

This paper describes a special-purpose digital processor for use in performing operations on sampled data. The processor is organized as multiple digital filters which can be grouped in cascade or canonic form. In addition, the weighting coefficients are modifiable in a self-adaptive mode during filter operations to form nonrecursive structures based upon the degree of coherency in two signal input channels. The adaptable system executes an LMS algorithm on a set of filter coefficients to perform, in real-time noise tracking and cancellation. An array with digital AGC, multiplier, interleaved memory and fixed-point processor are described.

A Real-Time Adaptive Predictive Coder Using Small Computers

This paper describes a real-time computer implementaation of a fourth-order adaptive predictive coder (APC) which transmits speech at 6400 bits/s. To reduce the demands on the central processor, the terminal uses the average magnitude difference function (AMDF) for pitch extraction and calculates the predictor coefficients and reflection coefficients assuming stationarity of the input data. With 16-bit fixed-point arithmetic processing, the coder achieves an intelligibility score of 87 percent on the diagnostic rhyme tests (DRT) and produces speech with acceptable voice naturalness even in the presence of acoustic background noise.

Digital matched filtering with pipelined floating point fast Fourier transforms (FFT's)

A special floating point arithmetic technique for fast Fourier transform (FFT) processors has been developed. The implementation of a high-speed pipeline FFT matched filter using the method employs significantly fewer components than a fixed-point processor with an equivalent performance level. The special floating point process avoids the nonlinear effects of fixed-point processors while achieving performance levels of traditional floating point arithmetic. Computer simulations were used to examine the performance of the system for linear FM pulse compression under a variety of conditions. In a specific case, with 8 bits plus sign quantization of the complex I- and Q-mantissa words in the processor and a 12-stage (4096-coefficient) FFT convolver, the mean square error (MSE) of the sidelobes relative to the peak from a single point target was less than -70 dB. Changes in waveform duration and sampling rate had negligible effect on the error level. This error characteristic can be treated as a computational or self noise, added to the input thermal noise of the radar receiver. Quantization artifacts or noise peaks which occur at levels consistent with the mantissa quantization are below levels (-50 dB for 8 bits plus sign) which would normally cause difficulty in an operational system.