Digital Signal Processing Assignment 7
Submit the assignment in the usual format.
- Do Mitra problem 7.25.
- Do Mitra problems 7.36 through 7.39 inclusive.
- Do Mitra problems 7.44 and 7.46 (and M 7.8).
- In our discussion of the one-pole resonator filter, we used the approximation
that B = 2(1-r). Show that B = -2 ln(r) is also a good approximation.
Plot Bandwidth B versus pole radius r using the exact expression and the
two approximations. Which approximation is valid over the longer range of values?
What happens to the exact expression when r is less than 0.172?
- In our discussion of the two-pole resonator filter, when the central frequency is
too close to DC, the frequency function becomes unsymmetric. Placing a zero at r = 1
reverses the direction of the asymmetry. This implies that there is a zero location,
less than 1, for which the filter is approximately symmetric. Find this zero
location for r = 0.99 and a center frequency of 0.05
radians.
- Write a Matlab program to generate damped sinusoids of 221 Hz,
442 Hz, and 884 Hz (sampled at 8000 Hz) with time constants of about 1
second. Space these notes about 4 seconds apart, and record them as a
wave file (.wav).
- Generate additional wave files of the same three notes,
reducing the time constant. Determine the time constant
(approximately) after which the notes sound more like a "click" than a
"pluck". At this point can you still distinguish the difference in
pitch?
Maintained by John Loomis,
last updated 5 Oct 2005