The Quantize Filter dialog lets you quantize the coefficients of the Inphase, Quadrature, or Complex filter in order to simulate a fixed-point representation. This allows you to analyze the frequency response of your filter for cases where you ultimately will implement it using fixed-point arithmetic.

The dialog asks " Quantize to How Many Bits?" . You enter an integer, N, and the program performs the quantization.

Also, a check box allows you to automatically save N in the options of the fractional file formats Text:Fract, Text:Hex, and Text:Binary.   If you use one of these formats, you generally will want to quantize the filter first in order to see the affect it will have on your filter response.

How the Quantization Algorithm Works

The quantization algorithm assumes the usual two's-complement fractional representation. For N bits, this system can represent numbers ranging from a minimum of -1.0 to maximum of just less than +1.0 (=(2^(N-1)-1)/(2^(N-1)), and the quantization algorithm assumes that the coefficients are in this range. Note that coefficients with magnitudes greater than 1.0 will be clipped by the quantization process, dramatically altering the filter response shape. So before you quantize, be sure to scale the gain of the filter so that all coefficients are within the fractional range.

Specifically, the quantization algorithm operates on each coefficient as follows:

• The coefficient is multiplied 2^(N-1).
• The result is rounded to an integer.
• If the result is greater than max (+2^(N-1) -1), it is clipped at max.
• Else if the result is less than min (-2^(N-1)), it is clipped at min.
• The result is divided by 2^(N-1).

Consider, for example, N=16 (the default value). A coefficient with a value of " 0.25" is unchanged by quantization, but a coefficient with a value of " 0.3" becomes " 0.299987792969" . Also, for N=16, the negative clipping value is -1 (as it is for any N), but the positive clipping value is (32767/32768 = +0.999969482).