I am new to DSP and I am trying to understand how to work with fixed point operations and in particular the Q31 format.

In floating point (full range) I am doing some multiplications, it could be for example 6.0 * 10.0 = 60.0. Converting this to Q31 would require first scaling it down to [-1,1) and then converting that to an int32_t (q31).

However when doing the same multiplication in Q31 we get a new Q31 result (after bit shifting properly), that can be taken back to float in the range [-1,1). But if I then scale that back up by reversing the original downscaling I do not end up with 60.

In summary:

• Downscale full range float to float in the range [-1,1) to be able to be represented in Q31
• Convert float in the proper range to Q31
• Perform fixed point multiplication (and possibly other unknown operations)
• Convert Q31 back to float
• Scale this float back up to the original range?

Is it possible to scale back to the original range somehow as in my last point - or is it a one-way conversion?

An example:

• Downscale: Input floats in an original range [0-5000] are scaled down to [-1,1). I tried with scaling function sign(val) * (abs(val) - min)/(max-min) where min is 0 and max 5000. This takes the values 6 and 10 to 0.0012 and 0.002.
• FloatToQ31: 0.0012 -> 2576980, 0.002 -> 4294967
• Multiply in Q31: 2576980*4294967 >> 31 = 5152
• Q31ToFloat: 5152 -> 2.39909e-06
• Upscale: Reversed downscale function val * (max - min) + min (again min=0, max=10000). This takes the value back to 0.0119954 which is not close to 60.

I am new to DSP and I am trying to understand how to work with fixed point operations and in particular the Q31 format.

In floating point (full range) I am doing some multiplications, it could be for example 6.0 * 10.0 = 60.0. Converting this to Q31 would require first scaling it down to [-1,1) and then converting that to an int32_t (q31).

However when doing the same multiplication in Q31 we get a new Q31 result (after bit shifting properly), that can be taken back to float in the range [-1,1). But if I then scale that back up by reversing the original downscaling I do not end up with 60.

In summary:

• Downscale full range float to float in the range [-1,1) to be able to be represented in Q31
• Convert float in the proper range to Q31
• Perform fixed point multiplication (and possibly other unknown operations)
• Convert Q31 back to float
• Scale this float back up to the original range?

Is it possible to scale back to the original range somehow as in my last point - or is it a one-way conversion?

An example:

• Downscale: Input floats in an original range [0-5000] are scaled down to [-1,1). I tried with scaling function sign(val) * (abs(val) - min)/(max-min) where min is 0 and max 5000. This takes the values 6 and 10 to 0.0012 and 0.002.
• FloatToQ31: 0.0012 -> 2576980, 0.002 -> 4294967
• Multiply in Q31: 2576980*4294967 >> 31 = 5152
• Q31ToFloat: 5152 -> 2.39909e-06
• Upscale: Reversed downscale function val * (max - min) + min (again min=0, max=5000). This takes the value back to 0.0119954 which is not close to 60.

I am new to DSP and I am trying to understand how to work with fixed point operations and in particular the Q31 format.

In floating point (full range) I am doing some multiplications, it could be for example 6.0 * 10.0 = 60.0. Converting this to Q31 would require first scaling it down to [-1,1) and then converting that to an int32_t (q31).

However when doing the same multiplication in Q31 we get a new Q31 result (after bit shifting properly), that can be taken back to float in the range [-1,1). But if I then scale that back up by reversing the original downscaling I do not end up with 60.

In summary:

• Downscale full range float to float in the range [-1,1) to be able to be represented in Q31
• Convert float in the proper range to Q31
• Perform fixed point multiplication (and possibly other unknown operations)
• Convert Q31 back to float
• Scale this float back up to the original range?

Is it possible to scale back to the original range somehow as in my last point - or is it a one-way conversion?

I am new to DSP and I am trying to understand how to work with fixed point operations and in particular the Q31 format.

In floating point (full range) I am doing some multiplications, it could be for example 6.0 * 10.0 = 60.0. Converting this to Q31 would require first scaling it down to [-1,1) and then converting that to an int32_t (q31).

However when doing the same multiplication in Q31 we get a new Q31 result (after bit shifting properly), that can be taken back to float in the range [-1,1). But if I then scale that back up by reversing the original downscaling I do not end up with 60.

In summary:

• Downscale full range float to float in the range [-1,1) to be able to be represented in Q31
• Convert float in the proper range to Q31
• Perform fixed point multiplication (and possibly other unknown operations)
• Convert Q31 back to float
• Scale this float back up to the original range?

Is it possible to scale back to the original range somehow as in my last point - or is it a one-way conversion?

An example:

• Downscale: Input floats in an original range [0-5000] are scaled down to [-1,1). I tried with scaling function sign(val) * (abs(val) - min)/(max-min) where min is 0 and max 5000. This takes the values 6 and 10 to 0.0012 and 0.002.
• FloatToQ31: 0.0012 -> 2576980, 0.002 -> 4294967
• Multiply in Q31: 2576980*4294967 >> 31 = 5152
• Q31ToFloat: 5152 -> 2.39909e-06
• Upscale: Reversed downscale function val * (max - min) + min (again min=0, max=10000). This takes the value back to 0.0119954 which is not close to 60.