Frequency Estimation Sampling Circuit Using Analog Hilbert Filter and Residue Number System

We describe a signal high-frequency estimation circuit using multiple low-frequency sampling circuits following an analog Hilbert filter and analog-to-digital converters (ADCs); here the sampling frequencies are relatively prime. Our proposed system is based on aliasing phenomena in frequency domain in waveform sampling and the residue number theory. A high frequency sampling circuit can directly estimate a high frequency input signal. However, handling of high frequency signals in electronic circuits is difficult and hence the proposed circuit is relatively easy to implement. Cosine wave with high frequency is provided as an input signal. Then cosine and sine signals with the same frequency are generated with an analog Hilbert filter (such as an RC polyphase filter) and they are fed into sampling circuits with different (relatively prime) and low sampling frequencies. Their analog outputs are analog-to-digital converted and for their digital outputs, complex FFTs are performed. Since the high frequency signal is sampled with low frequency clocks, the aliasing (spectrum folding) occurs. However, each aliased frequency is different because each sampling clock frequency is different in sampling circuits. Then according to the Chinese remainder theorem, the input frequency can be estimated. Notice that usage of the analog Hilbert filter is new in this paper; if the analog Hilbert filter is not used and the cosine input is directly sampled, the residue frequency cannot be obtained.