I am implementing an IIR controller in dsPIC 33EP (16-bit, fixed-point, two's complement, wrap-around, 40-bit accumulator, 32-bit multiply, 12-bit ADC) and I am using cascaded, Direct Form I second order sections (ordering up).

I am using Q15 (fractionals), but my coefficients are within the range +/-1. The question is: If a coefficient is exactly +1, will it fit in Q15?

The confusion is due to the fact that Q15 allows values from -1 to 0.99999999906 only. So I am afraid it will be quantized to 0 or -1 in 2's complement wrap-around.

I would very much appreciate any help.



There's an old trick you can use:

$$1\cdot x=x$$

So you don't need to multiply with a factor that equals $1$.


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