# HW 3 Q 6 rawspec.R JLCY, 19 Dec 2013

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rawspec = function(y, deltaT) {

    N = length(y)
    freqs = 2 * pi * (1:round((N/2)))/N
    plotfreqs = freqs/(2 * pi * (deltaT))
    nfreq = length(freqs)
    a = 1:nfreq
    b = 1:nfreq
    for (k in 1:nfreq) {
        a[k] = 2 * sum(y * cos(2 * pi * k * t/N))/N
        b[k] = 2 * sum(y * sin(2 * pi * k * t/N))/N
    }

    pgram = sqrt(a * a + b * b)/2

    pgram

}