Comparative Analysis of DTFT and DTFS in Compressed Sensing for Sparse Signal Reconstruction

Abstract

In the evolving landscape of signal processing, the efficient reconstruction of sparse signals from under-sampled data has garnered significant attention, especially within the compressed sensing framework. This paper compares the Discrete-Time Fourier Transform (DTFT) and Discrete-Time Fourier Series (DTFS) in sparse signal reconstruction. While DTFT and DTFS are cornerstone tools in signal analysis, their application to compressed sensing for sparse signal reconstruction remains relatively unexplored. This study aims to fill this gap by investigating how DTFT and DTFS can be leveraged to enhance the accuracy and efficiency of signal reconstruction under various conditions.

Extensive simulations using various sparse signal models reveal that DTFT is superior for continuous frequency spectra, while DTFS excels in periodic, discrete frequency components. A case study in biomedical signal processing, particularly Electrocardiogram (ECG) signal reconstruction, underscores the practical implications of our findings. Additionally, we explore the computational complexity of both methods, providing insights into their applicability in real-time scenarios. This paper provides a comparative framework and practical guidelines for selecting the appropriate transform in real-world scenarios.