Page 229 - DSP Integrated Circuits

214 Chapters Finite Word Length Effects

(binary) coefficients. One of the systems, Hjd eai, has, in principle, infinite data word
length while the other, HQ uant, has finite word length. In practice, the filters can be
implemented in a general-purpose computer using high-precision floating-point
arithmetic while the fixed-point arithmetic with quantization is simulated.
.rrouiems arising wiieii measuring
noise are that in certain cases the quanti-
zation, e.g., magnitude truncation, will
cause the two systems to have different
gains and that the output noise will be
correlated with the output signal. There-
fore, the difference in system gain and
the correlation with the input signal
must be removed. Further, some types of Figure 5.21 Measuring of round-off
quantization (for example, truncation) noise
cause a DC offset at the output. In speech
applications this offset should not be included in the noise, but in other applica-
tions it may be regarded as a major disturbance.
Comparison and measurement of the noise in different filter structures must
be done with respect to the dynamic signal range, i.e., the signal levels in the
structures shall be properly scaled. The loss in dynamic range can be measured as
described in Problem 5.7.

EXAMPLE 5.10
Determine the required internal data word length for the bandpass filter in Exam-
ple 5.6 when the dynamic signal range at the output should be at least 96 dB.
The losses in dynamic range were calculated in Example 5.8 to be 6.29 and
4.08 bits for the Loo-norm and Z/2-norm scaled filters, respectively. We define the
dynamic range of a sinusoidal signal as the ratio between the peak power of the
signal and the noise power. The largest output signal is

where the signal is represented with N bits, including the sign bit, and Q is the
quantization step. The power of the signal is

The dynamic range at the output of the filter is

Thus, we get

The required data word length inside the filter is estimated as