Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 43

EXAMPLE 2.11
If the analog signal to be quantized is a sinusoidal waveform, that is,

xðtÞ¼Asinð2p 1; 000tÞ

and if the bipolar quantizer uses m bits, determine the SNR in terms of m bits.
Solution:
Since x rms ¼ 0:707A and D ¼ 2A=2

m

, substituting x rms and D into Equation (2.28) leads to

0:707 A
2A=2 m

SNR dB ¼ 10:79 þ 20$log 10

¼ 10:79 þ 20$log 10 ð0:707=2Þþ20m$log 10 2

After simplifying the numerical values, we get

SNR dB ¼ 1:76 þ 6:02m dB (2.30)

EXAMPLE 2.12
For a speech signal, if a ratio of the RMS value over the absolute maximum value of the analog signal (Roddy and

x rms
jxj max

Coolen, 1997) is given, that is, , and the ADC quantizer uses m bits, determine the SNR in terms of m

bits.
Solution:
Since

x max x min
L

¼ 2j x j max
2 m

D ¼

substituting D in Equation (2.28) achieves

x rms
2jxj max =2 m

SNR dB ¼ 10:79 þ 20$log 10

x rms
jxj max

¼ 10:79 þ 20$log 10 þ 20mlog 10 2 20log 10 2

Thus, after numerical simplification, we have

x rms
jxj max

SNR dB ¼ 4:77 þ 20$log 10 þ 6:02m (2.31)

From Examples 2.11 and 2.12, we observed that increasing 1 bit of the ADC quantizer can improve
SNR due to quantization by 6 dB.