**EE342 Problem Set 9**

DUE W 04/14/1999

- 6.9d, g(d) - show results from hand work and matlab to verify dft()
function is working properly
- 6.10f
- 6.12 - plot magnitude spectrum of x[n] and answer questions
- 6.19
- 6.20a, b(i, ii)
- Consider the bird chirp data stored in the data file bird.dat. The data was obtained by recording three
chirps from a bird. After downloading the file from my web page into a
working matlab directory, it can be loaded into a matlab vector named
*bird* by typing **load bird.dat**. Verify the vector is
there and is the correct size by typing **whos**. You can then
listen to the chirps if your computer has a sound card and if your
version of matlab supports the *sound() * function by typing
**sound(bird,1/T)** where *bird* is the vector of recorded
data and *T* is the sampling interval. The microphone signal was
sampled at 8192Hz resulting in 4500 samples. To illustrate the use of
the DFT and the effect of aliasing perform the following operations.
Let matlab connect the data points in all plots with the *plot()*
function rather than *stem()* to keep the plots from looking too
messy.
- Plot the signal versus time.
- Using the DFT, plot the magnitude and phase spectra of the sampled signal
versus frequency in Hertz. What frequencies are the most prevalent?
- Reduce the sampling rate to 4096Hz by removing every other sample
in the signal. Plot the undersampled signal versus time.
- Using the DFT, plot the magnitude and phase spectra of the undersampled
signal versus frequency in Hertz.
- Comment on the effects of undersampling. If possible, listen to the
original signal as well as the undersampled signal to hear the effects.
- Separate the three chirps from the original signal sampled at 8192Hz
into three separate signals and plot each chirp's magnitude
spectrum versus frequency in Hz using the DFT. Based on this
spectral data can we distinguish which chirp we are looking at, i.e., can
we do bird word recognition?