Page 198 - DSP Integrated Circuits

Problems 183

(a) Draw a signal-flow graph for the FIR lattice filter.
(b) Determine the transfer function if N = 3.
4.7 View the DCT as an FIR filter bank and find possible reductions in the
computational complexity.

4.8 Why are doubly terminated reference filters used in the design of wave
digital filters? Is a Butterworth filter less or more sensitive to element errors
in the passband than the corresponding Chebyshev I filter?
4.9 Determine the ripple in the passband for a doubly terminated LC filter when
the reflection coefficient is 15%.
4.10 Which are the major factors that influence the passband sensitivity in a
doubly terminated LC filter?

4.11 Determine the relation between the group delays of an analog filter and the
corresponding digital filter that is obtained by bilinear transformation.
4.12 Determine the transfer function if each delay element in a filter structure is
replaced by a structure consisting of two delay elements and a sign
2
inversion, i.e., -z . Also, sketch the magnitude response of the filter if the
original filter was a lowpass filter.
4.13 Determine the reflectance function, S(z) = B\IAi, for the structure shown in
Figure P4.13. What kind of filter characteristic is realized? The detailed
wave-flow graph is also shown in Figure P4.13.

Fig. P4.13.