Sub-Nyquist Sampling and Measurement of FRI Signals With Additive Shot Noise

• Published in: IEEE transactions on instrumentation and measurement Vol. 72; pp. 1 - 11
• Main Authors: Yun, Shuangxing, Xu, Hongwei, Fu, Ning, Qiao, Liyan
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Algorithms; Annihilating filter method; Biomedical measurement; Circuits; Error analysis; Error correction; finite rate of innovation (FRI); Innovations; Low frequencies; Modulation; Noise measurement; parameter measurement; Pollution measurement; Process parameters; Robustness; Robustness (mathematics); Sampling; Shot noise; sub-Nyquist sampling; Time measurement; Trigonometric functions
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2023.3261912

To mitigate the impact of shot noise on the parameter measurement process of finite rate of innovation (FRI) signals, this article proposes a sub-Nyquist modulation sampling system with two measurement channels. The noisy signal is sampled in the main channel after being filtered by a sinc kernel to obtain the aliasing Fourier coefficients, whereas the FRI signal is shifted out of the baseband with a cosine modulation function in the accessory channel to expose the shot noise information to the low frequency band. The burst time parameters of shot noise can be estimated using the annihilating filter method from the samples in the accessory channel, while the parameters of the FRI signal will be measured from the observations in the main channel after the shot noise information has been removed. If the rate of innovation (RI) of the FRI signal is <inline-formula> <tex-math notation="LaTeX">\rho _{L} </tex-math></inline-formula> and is affected by <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> impulses of shot noise, the entire measurement process only requires <inline-formula> <tex-math notation="LaTeX">\rho _{L}\cdot \tau +2K </tex-math></inline-formula> points to be sampled per unit time <inline-formula> <tex-math notation="LaTeX">\tau </tex-math></inline-formula>. To enhance the robustness of the measurement process in actual circuit systems, a corrected annihilating filter method is proposed, and the parameter measurement error when employing this method is analyzed. Numerical and hardware experiments demonstrate that, compared to classical antinoise algorithms, the proposed method not only measures the parameters of FRI signals contaminated by shot noise more accurately, but also significantly improves the robustness of the measurement process in nonideal environments.