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Fig. 13-4. Example of Analog-to-Dlgltal Conversion for B Quantization Levels (3 bits).

The analog-to-digital converter divides the total amplitude range of the input sample into M quantizing levels, where M = 2", and n is the number of bits per sample. Assuming a uniform spacing of quantization levels, the maximum quantization error is ±0.5 A V where A V is the quantization step size, equal to Vpp / M = Vpp / 2", where Vpp is the full-scale input signal voltage.

* Harry Nyquist set the stage for modem digital communications with his classic paper, "Certain Topics on Telegraph Transmission Theory," published in the Transactions of American Institute of Electrical Engineers in 1928 (vol. 47, pp. 617-644).

It can be shown [Panter, 1965] that the mean-squared noise power due to quantization is (AV)2/12.The signal-to-quantization noise power ratio is (M2 - 1), which is approximately equal to M2 or 22n, assuming a uniform distribution of the input signal amplitudes over Vpp. See Table 13-4.*

TABLE 13-4. Required Bits Per Sample. The number of bits per sample is determined by the maximum quantization error and quantization noise allowed.

Number of Bits Per Sample

Maximum Quantization Error (%)

Signal Power to Quantization Noise Power Ratio* (dB)

0 0

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