How do I properly quantize an n-bit fixed-point data to m-bit fixed-point data with a bias (n>m) using the FI function from the Fixed-Point Toolbox 1.3 (R14SP3)?

I tried to use the following command to convert a 5-bit (3-bit fraction) fixed-point data to a 2-bit (1-bit fraction) fixed-point data with a bias:

E = fi([-0.25+0.125i;0.25-0.75i;0.5+0.875i;-0.25-0.5i;-0.5-0.125i;],1,5,3)

Q = numerictype(1,2,0.5,0.25)

a = fi(E,Q)

Where E is the input 5-bit (3-bit fraction) embedded.fi fixed-point data and Q is a embedded.numerictype object specifying a to be a 2-bit (1-bit fraction) embedded.fi fixed-point data with a bias of 0.25.

The resulting output fixed-point data a is not quantized correctly.

Answer 1

[MathWorks Support Team]

This enhancement has been incorporated in Release 2008a (R2008a). For previous product releases, read below for any possible workarounds:

The FI function is working as it is designed see the following example.

In the MATLAB command window:

a = fi(E,Q)

The issue is with the casting from a fixed-point data type to another fixed-point data type. MATLAB is actually processing the command in this manner:

a = fi(zeros(size(E)),Q)

a(:) = E;

The first command creates a fixed-point object with the attributes from numerictype Q and initializes all elements to be 0 (or 0.25 with the bias). The second command then converts the 5-bit fixed-point data E to the 2-bit fixed-point data a. The fixed-point conversion follows the fixed-point conversion arithmetic. It is outlined in the article attached in the resolution documents section.

To obtain the quantization that you are looking for, you should execute the following command:

b = fi(double(E),Q)

Which MATLAB processes as the following commands:

b = fi(zeros(size(E)),Q)

b(:) = double(E)