Page 237 - DSP Integrated Circuits

222 Chapter 5 Finite Word Length Effects

(d) Compare the three scaling procedures.
(e) Determine the round-off noise for the three filters in terms of SNR
assuming both rounding and truncation are performed after the
summation. Comment on the result!
5.7 Rank the different scaling criteria in terms of severity.

(a) Show that

(b) Show that

5.9 Scale the filter shown in Figure P5.9 usin^
(a) L2-norm scaling
(b) Loo-norm scaling

5.10 A properly scaled filter structure
generates low round-off noise, i.e.,
2
measurements show that c out is small. Figure P5.9 Direct form I
What conclusion can be drawn about the
coefficient word length required to satisfy
a stringent magnitude specification?

5.11 Scale the filter shown in Figure
P5.ll using the safe scaling
criterion. Also, determine the
coefficients if instead Loo-norm
scaling is used.
5.12 (a) Scale the filter shown in
Figure P5.12 using L%-
Figure P5.ll Cascade form
norms. The data word length
Wd is 8 bits, including the
sign bit. Two's-complement
representation is used. The
coefficients are
b = 0.98 and OQ = «i
For which type of input
signals is this scaling policy
appropriate?
(b) Also, determine the
variance for the round-off
noise at the output of the
filter when rounding is Figure P5.12 Direct form II
performed after the
multiplications.

characterizes a wide-band signal,
5.13 (a) Show that S x
(b) Show that SMI, characterizes a narrow-band signal.
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