Why does simulink generate warnings about quantization error when running my simulation?

In simulink I am making a filter using single precision coefficients. When I simulate the design I receive the following warning:

"The parameter's value cannot be represented exactly using the run-time data type. A small quantization error has occurred."

I am entering the coefficients into gain blocks, with the data type set to single precision. I believe that everything in my design is set to single precision. Is there a setting that I am missing that is causing the quantization error?

Answer 1

[Andy Bartlett]

Hi, I assume the coefficients have been entered using with MATLAB code like this

      coef = [0.05 0.15]

Since MATLAB defaults to double, these coefficients will be the most accurate representation of 0.05 and 0.15 that a double can hold. To see how close, you could do

mat2str(coef,18)
ans =
    '[0.0500000000000000028 0.149999999999999994]'

If you've constructed your model to use coef with single precision run-time parameters, then the original doubles will need to be quantized to singles. Under the hood, the Simulink model is doing the equivalent of

     runTimeCoef = single(coef)

To see what this produces, you could do

mat2str(runTimeCoef,18)
ans =
    '[0.0500000007450580597 0.150000005960464478]'

As you can see, the before and after values are difference.

        '[0.0500000000000000028 0.149999999999999994]'
        '[0.0500000007450580597 0.150000005960464478]'

Hence, the warning about precision loss.

One way to avoid this is to pre-quantized the coefficients before supplying them to Simulink

coef = single([0.05 0.15])

The parameter value used by the Simulink model will still be identical

'[0.0500000007450580597 0.150000005960464478]'

but the warning would go away.

As of R2016b, you can also suppress individual warnings after you've reviewed them and determined the warning to be benign.