Miscellaneous Exercises - Digital Signal Processing: An Introduction with MATLAB and Applications - page 299

Q36: Why do we need an adaptive delta modulation system? An adaptive
algorithm for the step size is given by: D n ¼ D n 1 K y ð n Þ y ð n 1 Þ , where K [ 1
is a constant. Implement this algorithm using DSP hardware. Draw the
block diagram of the adaptive modulator and the demodulator.
Q37: A block diagram of a sigma-delta modulator is shown below. Suggest a
decoder. Represent this system in Laplace domain and show how it can be
used for noise shaping (Fig. B.5 ).
Q38: Why is the sigma-delta modulator more appropriate for audio applications
than the delta modulator?
Q39: Design a circuit for DC blocking.
Q40: Design a digital SD modulator and demodulator.

Miscellaneous DSP Exercises: C

Q1: A fifth-order elliptic low-pass filter with the following specifications:

Pass-band peak-to-peak ripple = 0.5 dB
Minimum stop-band attenuation = 40 dB
The pass-band-edge frequency = 0.3p Use Matlab to implemented this filter
with second-order sections.

Q2: A 12-bit A/D converter is used to sample an analog signal. The sampled
signal x(n) is stored in the lower bits of DSP processor such that the
corresponding maximum dynamic range will be 1/16. Then x(n)istobe
passed to a 16-bit IIR filter whose transfer function is

1
1 0 : 98z 1 :

H ð z Þ¼

Scale the output signal such that its upper limit does not exceed unity.
Q3: Consider the first-order IIR filter described by the infinite-precision difference
equation

y ð n Þ¼ 0 : 625y ð n 1 Þþ x ð n Þ:

Show whether this system would trap into limit cycle when implemented
using 4-bit (a) rounding arithmetic, (b) truncation arithmetic. Let x(n) = 0 and
y(0) = 3/8. Find the magnitude and frequency of the oscillation for each case,
if any.
Q4: A

second-order IIR filter described by the following infinite-precision

difference equation

y ð n Þ¼ a 1 y ð n 1 Þ a 2 y ð n 2 Þþ x ð n Þ:

Derive the dead band bound that govern the occurrence of limit cycles in this
structure when implemented using rounding arithmetic.