function  halfspec(x)
%note that N must be even or this won't work.
N = length(x);
M = N/2 + 1;
X = fft(x);
P = abs(X).^2; 
P1 = P(1:M);
plot(1:M,P1) 
title('Single-Sided Amplitude Spectrum')
xlabel('freq number')
ylabel('|P1(f)|^2')
end