Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 552

11.23. Given the input data

xð 0 Þ¼ 25 xð 1 Þ¼ 30

and

determine the DCT coefficients.

11.24. Given the input data

xð 0 Þ¼ 25 ; xð 1 Þ¼ 30 ; xð 2 Þ¼ 28 ; xð 3 Þ¼ 25 ;
xð 4 Þ¼ 10 ; xð 5 Þ¼ 0 ; xð 6 Þ¼ 0 ; and xð 7 Þ¼ 0

determine the DCT coefficients X DCT ð 0 Þ , X DCT ð 2 Þ , X DCT ð 4 Þ , and X DCT ð 6 Þ .
11.25. Given the input data

xð 0 Þ¼ 25 ; xð 1 Þ¼ 30 ; xð 2 Þ¼ 28 ; xð 3 Þ¼ 25 ;
xð 4 Þ¼ 10 ; xð 5 Þ¼ 0 ; xð 6 Þ¼ 0 ; and xð 7 Þ¼ 0

determine the DCT coefficients X DCT ð 1 Þ , X DCT ð 3 Þ , X DCT ð 5 Þ , and X DCT ð 7 Þ .
11.26. Assume the following DCT coefficients with infinite precision:

X DCT ð 0 Þ¼ 14 ; X DCT ð 1 Þ¼ 6 ; X DCT ð 2 Þ¼ 6 ; and X DCT ð 3 Þ¼ 8

a. Determine the input data using the MATLAB function idct().
b. Recover the input data samples using the MATLAB function idct() if a bit allocation
scheme quantizes the DCT coefficients as follows: 2 magnitude bits plus 1 sign bit (3
bits) for the DC coefficient, 1 magnitude bit plus 1 sign bit (2 bits) for each AC coef-
ficient and a scale factor of 8, that is,

X DCT ð 0 Þ¼ 8 2 ¼ 16 ; X DCT ð 1 Þ¼ 8 1 ¼ 8 ; X DCT ð 2 Þ¼ 8 ð 1 Þ
¼ 8 ; and X DCT ð 3 Þ¼ 8 1 ¼ 8

c. Compute the quantized error in part (b) of this problem.
11.27. Assume the following DCT coefficients with infinite precision:

X DCT ð 0 Þ¼ 11 ; X DCT ð 1 Þ¼ 5 ; X DCT ð 2 Þ¼ 7 ; and X DCT ð 3 Þ¼ 3
a. Determine the input data using the MATLAB function idct().
b. Recover the input data samples using the MATLAB function idct() if a bit allocation
scheme quantizes the DCT coefficients as follows: 2 magnitude bits plus 1 sign bit
(3 bits) for the DC coefficient, 1 magnitude bit plus 1 sign bit (2 bits) for each AC
coefficient and a scale factor of 8, that is,

X DCT ð 0 Þ¼ 8 1 ¼ 8 ; X DCT ð 1 Þ¼ 8 1 ¼ 8 ; X DCT ð 2 Þ¼ 8 1 ¼ 8 ; and

X DCT ð 3 Þ¼ 8 0 ¼ 0

c. Compute the quantized error in part (b) of this problem.