Q-format conversion (fixed-point) to decimal (floating-point)

Dears,

I would like to convert the numbers (back and forth) between Qa.b format (fixed-point) and real-world numbers (floating-point): [-pi, pi] <-> [-2^17, 2^17 -1] as signed integers.

Is there any already exsisting Matlab function for it - if so, how to use?

Thank you!

[James Tursa]

Assuming you forgo the value of pi being represented (because top integer is 2^17-1 instead of 2^17), isn't this just multiply or divide by 2^17/pi? What am I missing here?

Answer 1

[Eswaramoorthy]

In MATLAB, you can use the 'fi' (fixed-point) data type along with its associated functions to convert between fixed-point and floating-point representations. However, there is no built-in function specifically designed to convert between the Q format (e.g., Qa.b) and real-world numbers. You would need to perform the conversion manually.

Here's an example of how you can do the conversion in MATLAB:

% Convert real-world number to fixed-point representation
realNumber = pi; % Input real-world number
Qa = 17; % Number of integer bits
Qb = 0; % Number of fractional bits
fixedPointNumber = fi(realNumber, true, Qa, Qb);

% Access the fixed-point value and scale it to the desired range
fixedPointValue = fixedPointNumber.data;
fixedPointRange = [-2^(Qa+Qb), 2^(Qa+Qb) - 1];
scaledValue = (fixedPointValue - fixedPointRange(1)) * (pi - (-pi)) / (fixedPointRange(2) - fixedPointRange(1)) + (-pi);

% Convert fixed-point representation back to real-world number
recoveredValue = scaledValue;

% Display the results
fprintf('Real-world number: %f\n', realNumber);
fprintf('Fixed-point value: %d\n', fixedPointValue);
fprintf('Scaled value: %f\n', scaledValue);
fprintf('Recovered real-world number: %f\n', recoveredValue);

In this code, we start by converting a real-world number (realNumber) to fixed-point representation using the fi function. The Qa and Qb parameters specify the number of integer and fractional bits, respectively.

Next, we access the fixed-point value using the '.data' property of the fixedPointNumber object. Then, we scale the fixed-point value to the desired range ([-pi, pi]) by mapping it from the range of the fixed-point representation ('[-2^(Qa+Qb), 2^(Qa+Qb) - 1]') to the real-world range.

To convert the fixed-point representation back to a real-world number, we simply assign the scaled value to recoveredValue.

You can modify the Qa and Qb parameters according to your fixed-point format requirements. The code provides the real-world number, fixed-point value, scaled value, and recovered real-world number for demonstration purposes.

Remember that fixed-point representation introduces quantization and may introduce rounding errors.