first, look at the spread of the values. Its around 6b for the integer portion (20 to -15). If you want 10b of fractional precision, then you have round((2**10) * k) for each of the values. This will give you a 16b value, where 1.0 = 1024 Keep in mind that "round" must be done carefully, as the implementation may result in the quantized coefficients giving an undesirable or even unstable impulse response. It is possible that you will need to round a 1.3 up to 2.0, or a 2.9 down to 2.0. Likewise, you might find that you'll want more fractional bits in order to allow the poles to be placed closer to the desired locations. In the hardware, you might have 12x16 multiplications. After the multiplication, you will need to (eventually) round the value by removing the lower bits. eg, a multiply by 1 would be x * 1024. the result would be 28b, and the lower 10b would be removed. This doesn't need to occur immediately though. you might have a 12x16 multiply (28b) followed by a 16b multiply (34b -- 20 fractional bits at this point). Eventually, you'll need to remove some fractional bits, as this is a recursive system.