Question

Write an M-file to produce a desired note, expressed in piano key number, for a given duration. Your M-file should be in the form of a function called key2note.m. Your function should have the following form:

        function xx = key2note(X, keynum, dur, fsamp)
        % KEY2NOTE Produce a sinusoidal waveform corresponding to a
        % given piano key number
        %
        % usage: xx = key2note (X, keynum, dur)
        %
        % xx = the output sinusoidal waveform
        % X = complex amplitude for the sinusoid, X = A*exp(j*phi).
        % keynum = the piano keyboard number of the desired note
        % dur = the duration (in seconds) of the output note
        % fs = sampling frequency, use 11025 or 22050 Hz
        %
        tt = 0:(1/fsamp):dur;
        freq =                   %<=============== fill in this line
        xx = real( X*exp(j*2*pi*freq*tt) );

For the “freq =” line, use the formulas given above to determine the frequency for a sinusoid in terms of its key number. You should start from a reference note (middle-C or A-440 is recommended) and solve for the frequency based on this reference. Notice that the xx = real( ) line generates the actual sinusoid as the real part of a complex exponential at the proper frequency. Show the code and play a note, say key #47 (G4), for 2 seconds to the instructor for verification.