小波分析作业

1. Matlab assignment: Fractional decimation rate

Write a Matlab program to achieve fractional decimation of the given man1.wav and

woman1.wav speech signals, and output the new wave files with rate of L / M, where L and M are integer, and L < M. The format of the function should be

wavedown ( inputfile, outfile, L, M)

The wav file can be read by wavread ( ) function, and wavwrite ( ) function can be used to create a new wav file. Please type “help wavread” or “help wavwrite” for their usage. These files can be played by many media players such as Windows Media Player, Real Player, and Quicktime Player.

Use the function firpm ( ) to design linear phase equiripple FIR filter for this problem. The order of the filter can be estimated using Kaiser’s formula

. 6.1413log 202110f

∆−−=δδ In this problem, we choose 01.021==δδ.

To simplify the problem, you can assume the input spectrum is bandlimited to M L /π (L < M) in order to achieve a decimation ratio of L/M.

If your Matlab does not have the signal Processing Toolbox, you need to write your own upsample and downsample functions, which are straightforward.

The convolution can be achieved by the conv ( ) function.

You need to scale the output data so that its maximal value is the same as that of the input. Otherwise you will find that the volume of the output file is lower than the input one.

In your report, list the order N of decimation ratios 2/3, 3/4, …, 9/10.

Use the function freqz ( ) to plot the frequency response of the filter for L/M = 2/3 and L/M=9/10.

Play the new wave file you generate with different L/M. Can you hear any difference from the original files for man1.wav and woman1.wav? Explain your observations in the report.