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====== Math 445 lecture 23: finding a frequency by interpolation ====== The following example shows how to use interpolation on discretized data to estimate the frequency of an oscillation. <code matlab> % Find the frequency of f(t) = -sin(omega t) by interpolation. % choose some fixed value of omega, then generate f(t) = -sin(omega t). omega = 0.87; t = linspace(0,10,20); f = -sin(omega*t); % plot f(t) plot(t, f, 'bo-'); grid on xlabel('x') ylabel('f(t) = -sin(omega t)') % get index n of first crossing from f positive to f negative n = find( f(1:end-1)> 0 & f(2:end) < 0); % interpolate t value of f(t) = 0 using data near that zero crossing T = interp1(f([n n+1]), t([n n+1]), 0); omega omega_estimated = 2*pi/T </code>