Input Coeffs

Fig. 7 shows a typical view of the b,a tab where you can view and edit the filter coefficients. Coefficient values are updated every time you design a new filter or update the poles / zeros.

Screenshot of the coefficients tab for floating point coefficients

Fig. 7 Screenshot of the coefficients tab for floating point coefficients

In the top row, the display of the coefficients can be disabled as a coefficient update can be time consuming for high order filters (\(N > 100\)).

Quantization format

By default, coefficients are displayed in float quantization format, the format returned by the filter design algorithm, with a selectable number of decimal places. Internally, full precision is always used.

However, many hardware platforms with limited computing resources like uCs can only perform fixpoint arithmetics. Here, scaling and wordlength have a strong influence on the obtainable accuracy.

It is important to understand that the quantization format only influences the display of the coefficients, the frequency response etc. is only updated when the quantize icon (the staircase) is clicked. Only when you do a fixpoint simulation or generate Verilog code from the fixpoint tab, the selected word format is used for the coefficients.

Fixpoint

When the format is set to fractional or integer, the fixpoint options are displayed as in Fig. 8. Here, the format Binary has been set.

Screenshot of the coefficients tab for fixpoint formats

Fig. 8 Screenshot of the coefficients tab for fixpoint formats (binary display)

Fixpoint Formats

Any other format (Binary, Hex, Decimal, CSD) is a fixpoint format with a fixed number of binary places which activates further display options. These formats (except for CSD) are based on the integer value i.e. by simply interpreting the bits as an integer value INT with the MSB as the sign bit.

The scale between floating (“Real World Value”, RWV) and fixpoint format is determined by partitioning the word length W into integer and fractional places WI and WF with total word length W = WI + WF + 1 where the “+ 1” accounts for the sign bit.

Three kinds of partioning can be selected in a combo box:

  • The integer format has no fractional bits, WF = 0 and

    W = WI + 1. This is the format used by amaranth as well, RWV = INT

  • The normalized fractional format has no integer bits, WI = 0 and

    W = WF + 1.

  • The general fractional format has an arbitrary number of fractional

    and integer bits, W = WI + WF + 1.

In any case, scaling is determined by the number of fractional bits, \(RWV = INT \cdot 2^{-WF}\).

\[c^2 = a^2 + b^2\]

In addition to setting the position of the binary point you can select the behaviour for:

  • Quantization: The very high precision of the floating point format

    needs to be reduced for the fixpoint representation. Here you can select between floor (truncate the LSBs), round (classical rounding) and fix (always round to the next smallest magnitude value)

  • Saturation: When the floating point number is outside the range of

    the fixpoint format, either two’s complement overflow occurs (wrap) or the value is clipped to the maximum resp. minimum (“saturation”, sat)

More info on fixpoint arithmetics can be found under Fixpoint Arithmetics.

Development

More info on this widget can be found under input_coeffs.