Filter Coefficients in MATLAB are always float data type

Question

I will be using the filter coefficients generated by MATLAB in my code that will run on a microcontroller. The poor microcontroller is very bad in floating point Arithmetic. So What do I do? Shall I directly truncate all float values to nearest int? shall I do ceil? or floor? Is there any function that can automatically do this conversion for me?

Update All my filter coefficeints are coming like: 0.465, 0.76, 0.23 etc, so If I use ciel then all will become zero. What should I do now?

Actual Filter Coefficients are:

> -0.00385638
>  0.004944457
>  0.01505063
>  0.018768283
>  0.009635631
> -0.01192891
> -0.035809426
> -0.045043857
> -0.023993426
>  0.032106934
>  0.111777547
>  0.18997355
>  0.238374966
>  0.238374966
>  0.18997355
>  0.111777547
>  0.032106934
> -0.023993426
> -0.045043857
> -0.035809426
> -0.01192891
> 0.009635631
> 0.018768283
> 0.01505063
> 0.004944457
> -0.00385638

Answer 1

Normally you would use fixed-point arithmetic for performing DSP on a a floating-point-challenged CPU.

So for, say, 16 bit fixed-point coefficients with a range of -1.0 to +1.0 your coeffs would translate to e.g.:

0.465    =>    0.465 * 0x7fff = 0x3b5

If your microcontroller does not have direct support for fixed point arithemtic (most DSPs do, general purpose microcontrollers typically do not) then you'll need to take care of scaling when you multiply or divide. (Addition and subtraction work as normal of course, provided you are not mixing different fixed point types.)

Answer 2

If your coefficients are contained in a vector "h," multiply them by 2^15, and use the int16() function.

For example:

coeffs = int16(h*2^15);

This will put them in an integer format filling the span of a 16 bit signed integer and from there you can export the coefficients to a header or delimited data file. The processor does not care whether they're integer or fractional. As far as it is concerned, it's just a binary pattern. It's up to the programmer to decide what those patterns mean.

Answer 3

Fixed point signal processing is a lot more complicated than floating point. The fixed point related problems include: quantization noise, coefficient quantization, overflow, underflow, saturation, limit cycles, etc.

For example, writing an IIR filter in fixed point, requires fairly thorough analysis of the filter topology, input & output signal statistics, state variable behavior and the filter transfer function as well.

Unless you have a very simple task, say a low order FIR filter with well known coefficients, I recommend some text book study.

Answer 4

You should use 2^^(number of fractional bits) For signed 16 bit with 15 fractional bits - you would multiply by 32768. The range is +32767 to -32768. 1/32768 is your lsb value. To convert a floating point to fixed - multiply as shown above and then round. Watch out for +1 since that is actually above 15 fractional and would require an integer bit. In your case you would saturate positive numbers to be no larger than 32767.