FIR II IP Core: User Guide

ID 683208
Date 8/14/2023
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3.4.1. Signed Fractional Binary

The FIR II IP core supports two’s complement, signed fractional binary notation, which allows you to monitor which bits the IP core preserves and which bits it removes during filtering. A signed binary fractional number has the format:

<sign> <integer bits>.<fractional bits>

A signed binary fractional number is interpreted as shown below:

<sign> <x1 integer bits>.<y1 fractional bits> Original input data

<sign> <x2 integer bits>.<y2 fractional bits> Original coefficient data

<sign> <i integer bits>.<y1 + y2 fractional bits> Full precision after FIR calculation

<sign> <x3 integer bits>.<y3 fractional bits> Output data after limiting precision

where i = ceil(log2ceil(number of coefficients/interpolation factor)) + x1 + x2

For example, if the number has 3 fractional bits and 4 integer bits plus a sign bit, the entire 8-bit integer number is divided by 8, which gives a number with a binary fractional component.

The total number of bits equals to the sign bits + integer bits + fractional bits. The sign + integer bits is equal to Input Bit WidthInput Fractional Bit Width with a constraint that at least 1 bit must be specified for the sign.