Contents

1 Basics

• MTF transform [1] performs a change in the representation of the symbols of a sequence, where those symbols that have a high probability of occurrency are “moved” in the source alphabet towards decreasing positions. Therefore, MTFT inputs $N$ symbols and output $N$ symbols.
• The output sequence has a probability density function which follows an exponential distribution with a slope $\lambda$:

  $$f\left(x\right)=\left\{\begin{array}{cc}\lambda e^{-\lambda x}\hfill & \text{if }x\ge 0;\hfill \\ 0\hfill & \text{if }x<0.\hfill \end{array}\right.$$

  (1)

  
  where $\lambda$ depends on the probability of ocurrence of the input symbols.

2 Forward transform

1. Create a list $L$ with the symbols of the source alphabet, where
   $$L\left[s\right]\leftarrow s;0\le s\le r.$$

2. While the input is not exhausted:
   1. $s\leftarrow$ next input symbol.
   2. $c\leftarrow$ position of $s$ in $L$ ($L\left[c\right]=s$).
   3. Output $\leftarrow c$.
   4. Move $s$ to the front of $L$.

2.1 Example

3 Inverse transform

1. The step 1 of the forward transform.
2. While the input is not exausted:
   1. $c\leftarrow$ next input code.
   2. $s\leftarrow L\left[c\right]$.
   3. Output $s$.
   4. The step 2.C of the forward transform.

3.1 Example

TO-DO

4 Lab

TO-DO

References