Matlab listing: oboeanal.m

The following Matlab script illustrates use of the findpeaks function above to determine the pitch of an oboe tone (given the general location of the correct spectral peak) and configure a spectrum analysis using the rectangular, Hamming, and Blackman windows. This script was used to create Figures 4.6 through 4.8.

diary './dia/oboeanal.dia';
diary on;

zpf = 5; % desired min zero-padding factor in all FFTs
fn = '../wav/oboe.ff.C4B4.wav';
[x,fs,nbits] = wavread(fn);
nx = length(x);
dur = nx/fs;
disp(sprintf(['Read %s, fs = %f, nbits = %d, ',...
              'length = %d samples = %0.1f sec'],...
             fn,fs,nbits,nx,dur));
soundsc(x,fs);
M = fs/10; % 100 ms window for pitch estimation
N = 2^nextpow2(M*zpf) % zero pad
Xzp = fft(x,N);

figure(K-1);
fmax = 500; % maximum freq in Hz
kmax = fmax*N/fs; % maximum freq in bins
prange = 1:kmax+1;
Xdb = dbn(Xzp(prange)); % dB normalized to 0 max
f = fs*[0:N-1]/N/1000; % frequency axis in kHz
plot(f(prange),Xdb);
ylabel('Magnitude (dB)');
xlabel('Normalized Frequency (cycles/sample)');
[amps,bins] = findpeaks(Xdb,1);
k0 = bins(1)-1;
f0 = k0*fs/N;
nP = fs/f0; % samples per period (used below)
disp(sprintf('Estimated pitch = %f Hz',f0));

% Test pitch estimate:
pause(ceil(dur)); % let previous sound finish
T = 1/fs;
t = 0:T:dur;
y = sawtooth(2*pi*f0*t);
sound(y,fs)

winnames = {'none','boxcar','none','hamming','none','blackman'};

% Configure window analysis

for K=[2 4 6]
  wintype = winnames{K};
  M = ceil(K*nP); % min Blackman length
  cmd = sprintf('w = %s(M);',wintype);
  eval(cmd);
  Nw = 2^nextpow2(M*zpf) % zero pad
  xw = x(1:M) .* w;
  Xwzp = fft(xw,Nw);
  %fmax = 5*f0; % maximum freq in Hz
  fmax = fs/4;
  kmax = fmax*Nw/fs; % maximum freq in bins
  prange = 1:kmax+1;
  Xwdb = dbn(Xwzp(prange)); % dB normalized to 0 max

  figure(K);
  subplot(2,1,1);
  plot(xw,'-k');
  axis tight;
  title(sprintf('Oboe data - %s window, K=%d',wintype,K));
  ylabel('Amplitude');
  xlabel('Time (samples)');
  subplot(2,1,2);
  f = fs*[0:Nw-1]/Nw/1000; % frequency axis in kHz
  plot(f(prange),Xwdb,'-k'); grid on;
  axis([f(prange(1)) f(prange(end)) -90 0]);
  ylabel('Magnitude (dB)');
  xlabel('Frequency (kHz)');

  plotfile = sprintf('../eps/oboe%s.eps',wintype);
  saveplot(plotfile);

end

diary off;

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.