Document Type : Original Research Paper

Authors

• A. Maroosi ¹
• H. Khaleghi Bizaki ²

¹ Department of Computer Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran.

² Department of Electrical and Computer Engineering, Malek Ashtar University of Technology, Tehran, Iran.

Abstract

Background and Objectives: Subsampling methods allow sampling signals at rates much lower than Nyquist rate by using low-cost and low-power analog-to-digital converters (ADC). These methods are important for systems such as sensor networks that the cost and power consumption of sensors are the core issue in them. The Chinese remainder theorem (CRT) reconstructs a large integer (input frequency) from its multiple remainders (aliased or under-sampled frequencies), which are produced from under-sampling or integer division by several smaller positive integers. Sampling frequencies can be reduced by approaches based on CRT.
Methods: The largest dynamic range of a generalized Chinese remainder theorem for two integers (input frequencies) has already been introduced in previous works. This is equivalent to determine the largest possible range of the frequencies for a sinusoidal waveform with two frequencies which the frequencies of the signal can be reconstructed uniquely by very low sampling frequencies. In this study, the largest dynamic range of CRT for any number of integers (any number of frequencies in a sinusoidal waveform) is proposed. It is also shown that the previous largest dynamic range for two frequencies in a waveform is a special case of our proposed procedure.
Results: A procedure for multiple frequencies detection from reminders (under-sampled frequencies) is proposed and maximum tolerable noises of under-sampled frequencies for unique detection is obtained. The numerical examples show that the proposed approach, in some cases, can gain 11.5 times higher dynamic range than the conventional methods for a multi-sensor under-sampling system.
Conclusion: Other studies introduced the largest dynamic range for the unique reconstruction of two frequencies by CRT. In this study, the largest dynamic ranges for any number of frequencies are investigated. Moreover, tolerable noise is also considered.

Keywords

• Chinese Remainder Theorem (CRT)
• Multi-sensor System
• Under Sampling
• Signal Reconstruction

20.1001.1.23223952.2023.11.2.17.9

Main Subjects

• Digital Signal Processing

Open Access

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Publisher

Shahid Rajaee Teacher Training University