Summary
Quantization is a representation of data samples with a certain number of bits per sample after rounding to a suitable level of precision. Quantization errors in a Digital Signal Processing (DSP) system can be introduced from three sources; one source is input quantization, a second is coefficient quantization and the third is the finite precision in the arithmetic operations [1]. The quantization error in the arithmetic operations can be controlled by carefully selecting the size of buffer registers according to the input word length. Quantization errors from input and filter samples are considered in this article. The effects of quantization errors and the tradeoffs required between precision and hardware resources are discussed in relation to the implementation of the DSP in Field Programmable Gate Array (FPGA). This article is divided into two main sections; quantization effects for upconversion and quantization effects for digital beamforming (DBF). Fixed length samples cause reduction in the filter dynamic range and gain resolution. We discuss finite precision effects on filter zeros and its frequency spectrum in section 2.1. Quantization error increases with filter order and this issue is described in section 2.2. Higher precision levels cause reduced quantization offsets. This is presented in section 2.3. Quantization produces similar effects in phased signals, however, its effects are different when considering multiple beam generation. Effects of precision levels on the beam patterns are described in section 3.1. In section 3.2, quantization effects are discussed for the first and second sidelobes.