Estimating Reflected Ultrasound Spectra from Quantized Signals

Quantization errors are inevitably introduced whenever analog-to-digital conversion of data is employed. The effect of these errors on estimating power spectra from ultrasound signals reflected from within the body is examined. Reflected data were simulated by convolving a pulse sequence with a filter model of the random reflectors encountered within the liver. The data were then quantized with an N-bit quantizer model, with 1 N 8, multiplied by a Hamming data window and used to estimate the power spectrum. For typical diagnostic signals reflected from 1 cm of tissue, the results indicate that the quantization errors limit the frequency range over which unbiased estimates of the spectra are observed for N 8. For N 8, the sidelobes in the Hamming window spectrum limit this range. To illustrate the implication of these results, the problem of estimating the slope of the acoustic attenuation coefficient, denoted by ß, for liver tissue from reflected ultrasound signals is examined. Three ßestimators are considered: 1) a new correlation method, 2) a zero-crossing count analysis, and 3) the slope of the log-spectral difference. The simulated results indicate under which conditions a particular ßestimator should be employed.