  Quantization plays a critical role in digital signal processing systems.
Quantizers are typically designed to obtain an accurate digital representation
of the input signal, operating independently of the system task, and are
commonly implemented using serial scalar analog-to-digital converters (ADCs).
In this work, we study hardware-limited task-based quantization, where a system
utilizing a serial scalar ADC is designed to provide a suitable representation
in order to allow the recovery of a parameter vector underlying the input
signal. We propose hardware-limited task-based quantization systems for a fixed
and finite quantization resolution, and characterize their achievable
distortion. We then apply the analysis to the practical setups of channel
estimation and eigen-spectrum recovery from quantized measurements. Our results
illustrate that properly designed hardware-limited systems can approach the
optimal performance achievable with vector quantizers, and that by taking the
underlying task into account, the quantization error can be made negligible
with a relatively small number of bits.
