Estudo e análise comparativa das técnicas de compressed sensing e subamostragem

Abstract

Multi-Frequency Bioelectrical Impedance Analysis has been applied to determine meat quality and skin cancer diagnosis. However, acquisition and characterization of multifrequency bioimpedance presents challenges, in particular due to the high sampling rates imposed on the analog-to-digital converter, which can lead to impractical low-cost implementations due to the need of more expensive converters. This work presents a study and a comparative analysis between two signal acquisition and processing techniques, which aim to reduce the sampling rate. The compressed sensing technique has an approach that diers from conventional methods, where signal projections are sampled. From the assumption that the signal is sparse in the frequency domain, the technique proposes signal acquisition with a waveform that have a dense representation in the frequency domain and the samples processing is performed by optimization algorithms. The undersampling system proposes applying a modied version of the discrete Fourier transform, where the input signal's frequency is known, which allows acquiring the phase and amplitude of the sampled signal with sampling rates below the Nyquist rate. Comparison between the two techniques shows that, inside the parameters and conditions assumed for bioimpedance acquisiton, the undersampling technique has advantages with respect to magnitude and phase errors as a function of input signal frequency and analog-to-digital converter resolution. With respect to magnitude, the undersampling technique shows the majority of the errors lie inside 1%, while the compressed sensing technique presents errors up to 4%. This work also an hardware implementation analysis, based on the assumption that the system will be implemented with the STM32F407VGT6 microcontroller. The undersampling technique also shows advantages, where the costs of the components necessary are about 10% of the compressed sensing technique's implementation cost. However, the hardware for implementation of the compressed sensing technique, the random demodulator, shows advantages to increase the sampling rate, allowing the acquisition of signals with frequencies higher than the undersampling system.