# Difference between revisions of "TDLT"

This page holds the results of Time Domain Lapped Transform (TDLT) optimization problems looking for integer transform coefficients that provide optimal coding gain. Wherever possible the assumptions are stated. Later we should include testing against actual image data to verify the results (see test data here).

The coding gain objective used as the objective is taken from slide 13 of Tim's presentation An Introduction to Video Coding

<need figure with block matrix diagrams>

The free parameters are initially just the coefficients p_0,...,p_m,q_0,...,q_m where m=(n/2)-1. We limit these to being dyadic rationals, e.g., x/2^d with d=6, between [-1,1].

Given p's and q's and assuming a linear ramp constrains the s's.

## 4x8

Optimal real-valued coefficients for V:

p0 = -0.18117338915051454

q0 = 0.6331818230771687

CG = 8.60603

p0 q0 s0 s1 CG
R=f -11/64
-0.171875
36/64
0.5625
91/64
1.421875
85/64
1.328125

8.63473
R=t,D=f -12/64
-0.1875
41/64
0.640625
92/64
1.4375
1093/768
1.423177

8.60486
R=t,D=t -16/64
-0.25
41/64
0.640625
92/64
1.4375
93/64
1.453125

8.59886

## 8x16

Optimal real-valued coefficients for V:

p0 = -0.39460731547057293

p1 = -0.33002212811740816

p2 = -0.12391270981321137

q0 = 0.822154737511288

q1 = 0.632488694485779

q2 = 0.40214668677553894

CG = 9.56867

p0 p1 p2 q0 q1 q2 s0 s1 s2 s3 CG
R=f
R=t,D=f -26/64
-0.40625
-22/64
-0.34375
-8/64
-0.125
53/64
0.828125
41/64
0.640625
26/64
0.40625
11/8
1.375
879/768
1.14453125
1469/1280
1.14765625
275/224
1.2276785714285714

9.56627
R=t,D=t -24/64
-0.375
-20/64
-0.3125
-4/64
-0.0625
53/64
0.828125
40/64
0.625
24/64
0.375
88/64
1.375
75/64
1.171875
76/64
1.1875
76/64
1.1875

9.56161