Page 238 - DSP Integrated Circuits

Problems 223

5.14 Determine the required order for a wave digital ladder filter of Cauer type that
meets the specification A max = 2 dB,A mi n = 70 dB,/" c = 50 kHz,/" s = 60 kHz,
and /"sample = 200 kHz. Now, assume that you are unable to find a set of
quantized coefficients with sufficiently short word length. Propose a remedy
to the problem.

5.15 Write a program to determine the DC offset at the output of the 1024-point
Sande-Tukeys FFT.
5.16 (a) Determine the coefficients for the one-dimensional MSDCT.
(b) Scale the coefficients.
(c) Determine the average value and variance of the round-off errors in the
two-dimensional DOT.
5.17 A bandpass filter is cascaded with a fifth-order allpass filter in order to
equalize the group delay. The allpass filter is realized by using first- and
second-order sections of type direct form I.
(a) Scale the allpass sections using a suitable Lp-norm for a wide band input
signal.
(b) Determine an ordering of the allpass sections that yields the best
dynamic signal range.
5.18 The requirement on a system for sampling an analog audio signal is very
high. The sample frequency is 44.1 kHz with an accuracy of 18 bits.
The following scheme is therefore proposed as an attempt to reduce the
cost and meet the stringent requirements on accuracy and the anti-aliasing
filter.
(a) Determine the required sample frequency such that the new system
generates equal or less quantization noise compared to the original
system.

Figure P5.18a

(b) Assume that the decimation is done by factor of 1024. Determine the
sample frequency and suggest a realization of the decimation filter that
has a low workload, i.e., operations per sample.

Figure P5.18b