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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def edf_simple(N, m, alpha):
 """Equivalent degrees of freedom. Simple approximate formulae. Parameters N : int the number of phase samples m : int averaging factor, tau = m * tau0 alpha: int exponent of f for the frequency PSD: 'wp' returns white phase noise. alpha=+2 'wf' returns white frequency noise. alpha= 0 'fp' returns flicker phase noise. alpha=+1 'ff' returns flicker frequency noise. alpha=-1 'rf' returns random walk frequency noise. alpha=-2 If the input is not recognized, it defaults to idealized, uncorrelated noise with (N-1) degrees of freedom. Notes ----- S. Stein, Frequency and Time - Their Measurement and Characterization. Precision Frequency Control Vol 2, 1985, pp 191-416. http://tf.boulder.nist.gov/general/pdf/666.pdf Returns ------- edf : float Equivalent degrees of freedom """


    N = float(N)
    m = float(m)
    if alpha in [2, 1, 0, -1, -2]:
        # NIST SP 1065, Table 5
        if alpha == +2:
            edf = (N + 1) * (N - 2*m) / (2 * (N - m))

        if alpha == 0:
            edf = (((3 * (N - 1) / (2 * m)) - (2 * (N - 2) / N)) *
                   ((4*pow(m, 2)) / ((4*pow(m, 2)) + 5)))

        if alpha == 1:
            a = (N - 1)/(2 * m)
            b = (2 * m + 1) * (N - 1) / 4
            edf = np.exp(np.sqrt(np.log(a) * np.log(b)))

        if alpha == -1:
            if m == 1:
                edf = 2 * (N - 2) /(2.3 * N - 4.9)
            if m >= 2:
                edf = 5 * N**2 / (4 * m * (N + (3 * m)))

        if alpha == -2:
            a = (N - 2) / (m * (N - 3)**2)
            b = (N - 1)**2
            c = 3 * m * (N - 1)
            d = 4 * m **2
            edf = a * (b - c + d)

    else:
        edf = (N - 1)
        print("Noise type not recognized. Defaulting to N - 1 degrees of freedom.")

    return edf