EE342 Problem Set 9

DUE W 04/14/1999

1. 6.9d, g(d) - show results from hand work and matlab to verify dft() function is working properly
2. 6.10f
3. 6.12 - plot magnitude spectrum of x[n] and answer questions
4. 6.19
5. 6.20a, b(i, ii)
6. 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?