CS525 S2006 Hw2 Solution

Solution to Homework #2: MIDI, Video Processing, and DCT

What is the main difference between a composite TV system and a component TV system? (See Page 25 of video.pdf.)
Ans: The composite TV system merges the video signal into one channel to be transmitted. The component TV system use 3 separate channels to transmit the video signal and resulting in better quality.
The video standards converts RGB signal to YIQ signal format. how can we take advantage of the YIQ format, in terms of video compression utilizing the human perception system? (See Page 26 of video.pdf).
Ans: When allocating bandwidth to these three video signal components, we can give more bandwidth to the luminance signal component (Y), less bandwidth to color components (IQ). Between I and Q compoments we can give more bandwidth to I.

Login to a machine in EN136 Lab (with Maple software). Follow the instructions in http://cs.uccs.edu/~cs525/dct/dctmws.htm to generate the FDCT results their plots.
Create a 8x8 pixel data matrix of your choice using the fuction similar to
bwstrip:=proc(f)
local i,j;
for i from 1 to 8 do
for j from 1 to 8 do
    if (i mod 4 > 1) then f[i,j]:=0;
    else f[i,j]:=100;
    fi;
od;
od;
end;
bwstrip(f);
It can be an area with gradient value changes from left to right, such as
gradient:=proc(f)
local i,j;
for i from 1 to 8 do
for j from 1 to 8 do
f[i,j]:=10*j;
fi;
od;
od;
end;
gradient(f);
execute getdctf(F); to obtain the 2D-DCT coefficients in F matrix.
Use print(F); to print the matrix and matrixplot(f, axes=BOXED); to plot the resulting matrix.
Submit the F matrix, the corresponding zig-zag sequence, and the Intermediate sequence for the above zig-zag sequence (values encoded using the VLI encoding), the compression ratio for this particular data set.
Ans:
Blocking: The following are the 8x8 block data for a block in a Q plane. It has a vertical line pattern.

Fast DCT: For the above block, what are the corresponding 8x8 transformed coefficients? Express them in matrix format.

Threshold and Quantization Step: Round the coefficients to the nearest integer numbers.
Zig-zag sequence: Describe the order of coefficients after arranging them in the zig-zag sequence.

Ans: 400, 43, 4 zeros, 51, 8 zeros, 76, 12 zeros, 217, EOB

Run length and VLI Coding: Encode the intermediate sequence in (size, magnitude), (runlength, size, magnitude)+ symbol using runlength and VLI coding. Describe each data pattern of these fields in its equivalent decimal value.

Ans: (9, 400), (0, 6, 43), (4, 6, 51), (8, 7, 76), (12, 8, 217), (0, 0)

4 + 9 + 4+4+6 + 4+4+6 + 4+4+7 + 4+ 4+ 8 + 4+4=80 bits

Assume each of original source 8x8 block data is 8 bit, the runlength and size field are 4bits without using VLC Huffman coding, magnitude fields are encoded with VLI code. What is the compression ratio between the original data size and the encoded intermediate encoded sequence?

Ans: 64*8:80=512:80=6.4

If all elements of a JPEG block have the same non-zero value. How many zeros will appear in the transformed coefficients?
Ans: 63 zeros.

gradient := proc(f)
local i, j;
for i to 8 do for j to 8 do f[i, j] := 10*j end do end do
end proc

> gradient(f); print(f); matrixplot(f, axes=BOXED);

gradient f data

gradient f plot

> getdctf(F); print(F); matrixplot(F, axes=BOXED);

gradient IF data with ZigZag sequence

Threshold and Quantization Step: Round the coefficients to the nearest integer numbers.
Zig-zag sequence: Describe the order of coefficients after arranging them in the zig-zag sequence
Ans: 360, -182, 4 zeros, -19, 8 zeros, -6, 12 zeros, -1, EOB.

gradient IF plot

Run length and VLI Coding: Encode the intermediate sequence in (size, magnitude), (runlength, size, magnitude)+ symbol using runlength and VLI coding. Describe each data pattern of these fields in its equivalent decimal value.
Ans: (9,360), (0, 8, 73), (4, 5, 12), (8, 3, 1), (12,1,0), (0,0).
The number of bits encoded:
4+9+ 4+4+8+ 4+4+5+ 4+4+3+ 4+4+1+4+4=70.
Assume each of original source 8x8 block data is 8 bit, the runlength and size field are 4bits without using VLC Huffman coding, magnitude fields are encoded with VLI code. What is the compression ratio between the original data size and the encoded intermediate encoded sequence?

Ans: 64*8:70=512:70=7.31