(a) For fo = 1/50 and N = 200, write a program to quantize the signal x(n), using truncation, to 64, 128, and 256 quantization levels In each case plot the signals x(n), tg(n), and e(n) and compute the corresponding SQNR. (b) Repeat part (a) by using rounding instead of truncation. (c) Comment on the results obtained in parts (a) and (b).

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1.16 Quantization enor in A/D conversion of a sinusoidal signal Let x,(n) be the signal
obtained by quantizing the signal x(n) = sin 27 fon. The quantization error power
P, is defined by
N-1
N-1
1
(n) = E (n) – x(n))
The "quality" of the quantized signal can be measured by the signal-to-quantization
noise ratio (SQNR) defined by
SONR = 10log10
Pa
where P, is the power of the unquantized signal x(n).
(a) For fo = 1/50 and N 200, write a program to quantize the signal x(n), using
truncation, to 64, 128, and 256 quantization levels In each case plot the signals
x(n), 1q(n), and e(n) and compute the corresponding SQNR.
(b) Repeat part (a) by using rounding instead of truncation.
(c) Comment on the results obtained in parts (a) and (b).
(d) Compare the experimentally measured SQNR with the theoretical SQNR pre-
dicted by formula (14.32) and comment on the differences and similarities.
Transcribed Image Text:1.16 Quantization enor in A/D conversion of a sinusoidal signal Let x,(n) be the signal obtained by quantizing the signal x(n) = sin 27 fon. The quantization error power P, is defined by N-1 N-1 1 (n) = E (n) – x(n)) The "quality" of the quantized signal can be measured by the signal-to-quantization noise ratio (SQNR) defined by SONR = 10log10 Pa where P, is the power of the unquantized signal x(n). (a) For fo = 1/50 and N 200, write a program to quantize the signal x(n), using truncation, to 64, 128, and 256 quantization levels In each case plot the signals x(n), 1q(n), and e(n) and compute the corresponding SQNR. (b) Repeat part (a) by using rounding instead of truncation. (c) Comment on the results obtained in parts (a) and (b). (d) Compare the experimentally measured SQNR with the theoretical SQNR pre- dicted by formula (14.32) and comment on the differences and similarities.
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