1 Frequencial Masking

The HAS (Human Auditory System) has a finite frequency resolution, which basically means that weaker audio signal (maskee) becomes inaudible in the presence of (is masked by) a louder audio signal (masker), when they are close enough [1], in the frequency domain (and obviously in time, i.e., in the same chunk). When this happens, the subband [2] in which the maskee signal is placed can be quantized more severely without perceiving the quantization noise in the maskee subband (see Figure 1).

2 A dynamic computation of the Quantization Step Sizes

1. Given a decomposition of a chunk $\mathbf{W}=\{{\mathbf{w}}_s\}$, determine the energy $\{E({\mathbf{w}}_s)\}$ of each subband. For this is a good idea to have the same bandwidth in all the subbands.

2. Find the subband with the highest energy:

   $$\begin{array}{}\text{(1)}& {\mathbf{w}}_m=\underset{{\mathbf{w}}_i\in \mathbf{W}}{\arg \max }E({\mathbf{w}}_m):=\{{\mathbf{w}}_{\ast }\in \mathbf{W}:E({\mathbf{w}}_i)\le E({\mathbf{w}}_m)\text{ for all }{\mathbf{w}}_i\in \mathbf{W}\}.\end{array}$$

3. Being ${\mathbf{\Delta }}_m$ the current QSS of the subband ${\mathbf{w}}_m$, compute the set of optimal¹ QSSs as

   $$\begin{array}{}\text{(2)}& {\mathbf{\Delta }}^{\ast }:=\{\cdots ,3{\mathbf{\Delta }}_{m-2},2{\mathbf{\Delta }}_{m-1},{\mathbf{\Delta }}_m,2{\mathbf{\Delta }}_{m+1},3{\mathbf{\Delta }}_{m+2},\cdots \}.\end{array}$$

3 Deliverables

Implement the algorithm described in Section 2 in a module named simultaneous_masking.py to be used in the InterCom.

Mark: 10 points.

4 Resources