MMA410  Fourier and Wavelet Analysis
About Assignement 1
A first exercise
If you wish to do something more fun than just plotting sinfunctions
and their spectra (i.e. the Fourier transform), you could do
something like this.
 Take a sound recording in a suitable format, and use matlab
to sample it. I have here the beginning of one of my daughter's
disks, croc1.wav , which you also could download.
 With matlab, use the command [crs,Fs,bits] =
wavread('filename')
Then the varable crs will contain the sampled
values, Fs will contain the sample rate, and bits
will contain the number of bits stored in each sample. In my
case the sample rate is about 11000, and the number of bits is
8. Its a monosignal, and so crs happens to be
a 46456x1 vector (the wavefile corresponds to about 4 seconds
of music)
 Now you can plot the signal, most easily just do
plot(crs)
 Next try to find the spectrum of this signal:
crocspec = fft(crs);
plot(abs(crocspec))
 We now do a most trival kind of filtering (but think of why I
did it this way, and how it should really be done!)
crocspec2 = crocspec;
crocspec2(5000:464565000) = 0; (what does
this imply?)
crs_filtered = ifft(crocspec2);
plot(abs(crs_filtered))
wavwrite(abs(crs_filtered),Fs,bits,'croc_filtered.wav')
 If you happen to do this on a pc, you chould be able to
listen to the two .wavfiles and hear the difference.
 It should also be possible to listen to the filtered signal
directly by using the command
sound(crs_filtered,Fs,bits); this might work directly on
the unixcomputers.
To create and use filters
Note that this is not a course in the theory of filters ....
 The matlab function filter can be used to pass a
digital signal, such as the crocsample that was created
above. The usage is
crs_filter1 = filter(num,1,crs);
and then you can look at this file, directly, or at the spectrum
after passing the signal through fft as above.
 The first to arguments to filter are the parameters
that define the filter. The filter is defined by a rational
function, i.e. the quotient of two polynomials. If the denominator
is identically 1 as in the example, the filter is of type
"FIR". The vector num determines if it is a high pass or
low pass or other kind of filter.
 The vector num can be created in the following way.
 Open the Digital Filter Design & Analysis Tool by
typing fdatool in matlab.
 You will then find a graphical user interface, where you
can experiment with different parameters, and create different
types of design. Note that for the example above, it is useful
to set Fs = 11025.
 When you are happy with the paramaters, click Design filter
 .... and then export the result using the Filemenu:
Export. Use Export to workspace.
 Some examples are available in the file filtercoefficienter.mat that
you can put in your matlabdirectory. After typing load
filtercoefficienter you should have two variables
Num1 and Num2 that you can use with the filter
command. One of them is a high pass filter, and the other is a low
pass filter of high orders.
