Efficient Reconstruction of Narrowband Signals Using Multifrequency Undersampling Techniques

This paper presents a novel approach to the reconstruction of narrowband signals using undersampling techniques. Traditional sampling methods, which adhere to the Nyquist theorem, often require high sampling rates, leading to increased costs and data processing demands. In contrast, undersampling techniques can significantly reduce these requirements by sampling at rates lower than the Nyquist frequency. This work leverages the principles of compressive sensing to reconstruct frequency-sparse signals by sampling them at multiple distinct frequencies. The proposed method ensures accurate signal reconstruction by using Alias Prediction Diagrams (APDs) and their generalized form, Widened APDs (WAPDs), to predict the positions of aliases generated during the sampling process. The criteria for selecting appropriate sampling frequencies are derived, ensuring that the original signal can be accurately reconstructed even when composed of multiple narrowband components. The effectiveness of the proposed method is validated through experimental results obtained from a test bench capable of measuring signals up to 18GHz using sampling frequencies between 50MHz and 120MHz. The results demonstrate the successful reconstruction of signals with up to seven narrowband components, each with a bandwidth of around 150 kHz. Additionally, the proposed method offers significant reductions in acquisition, transmission, processing, and storage rates compared to direct sampling techniques; in the proposed setup these rates are reduced up to 1/300 of the direct sampling rates. This work provides a robust framework for efficient signal reconstruction in applications where reducing acquisition, processing and storage rates is crucial.