function [f, A] = plate_spectrum(t, x)
% PLATE_SPECTRUM  One-sided amplitude spectrum of a real, uniformly sampled signal.
%
%   [f, A] = plate_spectrum(t, x) applies a Hann window and returns the
%   amplitude A at frequencies f [Hz], scaled so that a steady sinusoid of
%   amplitude a shows a peak of height about a.  For a decaying signal the
%   peak heights depend on the record length, so compare shapes and
%   frequencies rather than absolute heights.

x = x(:).';
N = numel(x);
dt = t(2) - t(1);
win = 0.5 * (1 - cos(2 * pi * (0:N - 1) / (N - 1)));
X = fft(x .* win);
nh = floor(N / 2) + 1;
X = X(1:nh);
A = abs(X) * 2 / sum(win);
f = (0:nh - 1) / (N * dt);
end