PURPOSE
The purpose of this laboratory is to design and implement a routine that will resample (upsample and/or downsample) a sequence.
ASSIGNMENT
1. Answer in writing all the questions in the "Some questions" sections of the Downsampling and Upsampling links, above.
2. Write a MATLAB function, named resample, which has the following first lines:
function y = resamp(x, r)
% RESAMP Resample an input sequence x by a factor of r
% to produce an output sequence y by a combination of upsampling and downsampling.
% For example,
% y=resamp(x,1.5);
% will upsample x by 3 and downsample by 2.
o x is just an plain-vanilla array, not one of our Matlab sequence structures.
o You may want to look at the MATLAB function rat, which tries to express a rational number (such as the resampling parameter, r) as the ratio of integers.
o You may use the MATLAB functions fir1, filter and/or kaiser, to make your Kaiser filter only.
o Obviously you may not use the MATLAB resample, decimate, or interpolate functions. However, you should feel free to use these functions to check your resamp function. You should read about making the Kaiser filter here.
o You will want to make sure that the bandwidth and gain of your Kaiser filter are correct, given the value of your resampling parameter, r.
o You may use MATLAB's conv routine if you wish.
3. Test your resamp against MATLAB's resample function. Since MATLAB's resample function may use a different lowpass filter, we can't simply compare point by point.
However, we can look at the output of the two functions for a simple sinusoidal input to see that it does the right thing. Here is a small program called test_resamp to do just that. What test_resamp does is to take an input sequence and plot the first few points resampled by a given factor using both Matlab's resample function and your test_resamp function. To use test_resamp, just put it in the directory with your resamp function, and run it. For example, to test upsampling of a little sin sequence by a factor of two, just do this:
>> x = -sin(2 * pi * (0:10) / 4);
>> test_resamp(x, 2);
The output of your resamp function is in blue and the output of matlab's resample function is in red. They should match very well. You can do help test_resamp to find out the other arguments of the function.
4. Test your resamp function by upsampling or downsampling a segment of speech. You can get this sample in several ways:
o Take my speech sample, seashell .wav, which we played earlier.
o Find another . wav file on the net
o Record your own . wav file.
5. Once you have a .wav file, read the data into your program using MATLAB's wavread function.
6. Resample x to some other, non-integer rate, using your resamp function: y = resamp(x, 1.5);
7. To check that you resampled correctly, playback the resampled signal using the ,,oundsc function at the new sample rate, for example: soundsc(resamp(x, 1.5), 1.5 * fs);
The resampled function should sound very similar to the original function, at least if it is upsampled.
8. You should download the following file and put it in your directory : lab5.m. Then type publish lab5, print the output, and submit it.