Abstract
This paper describes a system for ultrasonic wave attenuation measurements which is based on pseudo-random binary codes as transmission signals combined with on-the-fly correlation for received signal detection. The apparatus can receive signals in the nanovolt range against a noise background in the order of hundreds of microvolts and an analogue to digital convertor (ADC) bit-step also in the order of hundreds of microvolts. Very high signal to noise ratios (SNRs) are achieved without recourse to coherent averaging with its associated requirement for high sampling times. The system works by a process of dithering – in which very low amplitude received signals enter the dynamic range of the ADC by 'riding' on electronic noise at the system input. The amplitude of this 'useful noise' has to be chosen with care for an optimised design. The process of optimisation is explained on the basis of classical information theory and is achieved through a simple noise model. The performance of the system is examined for different transmitted code lengths and gain settings in the receiver chain. Experimental results are shown to verify the expected operation when the system is applied to a very highly attenuating material – an aerated slurry.
Highlights
This paper describes an ultrasonic spectrometer for measurements of compression wave attenuation and phase speed as functions of frequency at very much higher signal to noise ratios (SNRs) than would be expected from a conventional system based on a high voltage pulser-receiver
Concluding remarks We have discussed the theory and performance of a coded sequence ultrasonic spectrometer and have demonstrated that it can receive signals which are very much lower in amplitude than both the noise at the input of the system and the analogue to digital convertor (ADC) bit-step. This performance was achieved by a process of dithering whereby the input signal rides on the input noise to reach into the dynamic range of the ADC
The setting of the amplitude of this noise was crucial to the effective operation of the system and necessitated an input amplifier to supply noise of the appropriate amplitude – the standard deviation being equal to the ADC bit-step
Summary
This paper describes an ultrasonic spectrometer for measurements of compression wave attenuation and phase speed as functions of frequency at very much higher signal to noise ratios (SNRs) than would be expected from a conventional system based on a high voltage pulser-receiver. The integration process implicit in the cross-correlation operation (accumulation in digital terms) reduces this noise considerably, leaving the required signal component expressed over several bits of the ADC output, even though its initial amplitude was very much less than a single ADC bit-step. 5. Optimum noise level Figure 4 illustrates the quantisation process that underpins the operation of the ADC; the horizontal axis represents the input signal amplitude and the vertical axis represents the digitised result. The curve for 0.5 is under sampled and that for 10 is over sampled We have simulated this digitising process [2] in order to assess the extent to which the input noise passes through the ADC to produced digitised output noise of the same amplitude for different Golay sequence lengths N. High sequence lengths imply long acquisition times, so there is a practical limit which will derive from a combination of the time available for measurement and the stationarity of the physical properties of the test medium
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