When the Best Precision Fractional Length option is selected, the coefficient fractional width is set to maximize the precision of the specified filter coefficients. As discussed in the Quantize Only section, the FIR Compiler analyzes the filter coefficients to determine how many bits are required to represent the integer portion of the coefficient values. All the remaining coefficient bits are then allocated to represent the fractional portion of the coefficients. When all the specified coefficients are between 1 and -1, only a single integer bit is required. The reminder of the coefficient word is then used for fractional bits. When the coefficient range reduces further, the fractional bit width is specified to a value greater than or equal to the coefficient width; otherwise the coefficient values contains redundant information that does not need to be explicitly stored. The available coefficient bits can then be better used to increase the precision of the coefficient values. This section goes on to illustrate this concept further. The MathWorks Fix Format notation is used, Fixword length _ fractional length . The word length is specified by the Coefficient Width parameter, and the fractional length is specified by the Coefficient Fractional Bits parameter.
In This Figure the coefficient values are represented using 18 bits. The binary point is positioned such that 17 bits are used to represent the fractional portion of the number. An analysis of the coefficients reveals that no value has a magnitude greater than 0.25; therefore, the upper two MSBs are a sign extension and contain redundant information.
In This Figure , 16 bits are used to represent the same coefficient values to the same precision. The redundant information has been removed, reducing the resources required to store the filter coefficients. The binary point position has not moved. 17 bits are still effectively used to represent the fractional portion of the number, but one of them does not need to be explicitly stored, as it is a sign extension of the stored MSB.
In This Figure 18 bits are specified for the coefficient width. The two additional bits can be used to increase the precision. The binary point position has still not moved, but now, 19 bits are effectively used to represent the fractional portion of the number, which results in an increase of the filter precision.