Digital Signal Processing Reference
In-Depth Information
10. Given the input signal x[n] = 2 cos(2100n=300) + cos(2110n=300=8) for
n = 0::255, write the commands to nd the DWT for 3 octaves. Compare
your results with those of the dwt function. Plot the original function, as well
as the approximate signals.
1
11. For the Haar transform show in Figure 9.4, use values a = b =
2
(no down-
sampling), nd signals z, w, and y, given an input of x =f6, 1, 3, 7, 2, 5, 8,
10g.
12. Suppose you have a 3-octave DWT. Draw the analysis structure in terms of
lters and down-samplers.
13. For a four-octave DWT, suppose the input has 1024 samples. How long would
the detail outputs be? How long would the approximate outputs be? What
if down/up-sampling were not used? For simplicity, you can assume that the
lter's outputs are the same lengths as their inputs.
14. For an input of 1024 samples, how many octaves of the DWT could we have
before the approximation becomes a single number? For simplicity, you can
assume that the lter's outputs are the same lengths as their inputs.
15. We stated above that the quadrature mirror lter will not work for four co-
ecients, i.e., h
0
= g
0
=fa;b;c;dg, h
1
=fa;b;c;dg, g
1
=h
1
. Show
analytically that this will not work. That is, what constraints are there on the
values a, b, c, and d, in order to get perfect reconstruction?
