The easiest way I can think of is to find the zero-crossings of the signal and take the inverse to calculate the frequency.
Example:
x = linspace(0,10*pi,1E+5); % Create Data
y = sin(1./(x+0.01)); % Create Data
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0); % Returns Approximate Zero-Crossing Indices Of Argument Vector
dy = zci(y); % Indices of Approximate Zero-Crossings
for k1 = 1:size(dy,1)-1
b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)]; % Linear Fit Near Zero-Crossings
x0(k1) = -b(1)/b(2); % Interpolate ‘Exact’ Zero Crossing
mb(:,k1) = b; % Store Parameter Estimates (Optional)
end
freq = 1./(2*diff(x0)); % Calculate Frequencies By Cycle
figure(1)
plot(x, y)
hold on
plot(x0, zeros(size(x0)), '+r')
hold off
grid
axis([0 1 ylim])
The ‘freq’ calculation multiplies the difference by 2 because it is actually calculating the half-cycle frequencies otherwise. To calculate the full-cycle frequencies (the correct result), it is necessary to multiply the half-cycle frequencies by 2.
The plot simply demonstrates that the linear interpolation is approximately accurate. It is not necessary for the code.
I don’t have your data, but it should work with it. It might give an anomalous result for the end value because it may calculate a zero-crossing there even if there is not one. Just discard it. My code is reasonably robust but cannot account for absolutely all possible conditions with such real-world data.
