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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 inverse_spectrum_truncation(psd, max_filter_len, low_frequency_cutoff=None, trunc_method=None):
 """Modify a PSD such that the impulse response associated with its inverse square root is no longer than `max_filter_len` time samples. In practice this corresponds to a coarse graining or smoothing of the PSD. Parameters psd : FrequencySeries PSD whose inverse spectrum is to be truncated. max_filter_len : int Maximum length of the time-domain filter in samples. low_frequency_cutoff : {None, int} Frequencies below `low_frequency_cutoff` are zeroed in the output. trunc_method : {None, 'hann'} Function used for truncating the time-domain filter. None produces a hard truncation at `max_filter_len`. Returns ------- psd : FrequencySeries PSD whose inverse spectrum has been truncated. Raises ------ ValueError For invalid types or values of `max_filter_len` and `low_frequency_cutoff`. Notes ----- See arXiv:gr-qc/0509116 for details. """

    # sanity checks
    if type(max_filter_len) is not int or max_filter_len <= 0:
        raise ValueError('max_filter_len must be a positive integer')
    if low_frequency_cutoff is not None and low_frequency_cutoff < 0 \
        or low_frequency_cutoff > psd.sample_frequencies[-1]:
        raise ValueError('low_frequency_cutoff must be within the bandwidth of the PSD')

    N = (len(psd)-1)*2

    inv_asd = FrequencySeries((1. / psd)**0.5, delta_f=psd.delta_f, \
        dtype=complex_same_precision_as(psd))

    inv_asd[0] = 0
    inv_asd[N//2] = 0
    q = TimeSeries(numpy.zeros(N), delta_t=(N / psd.delta_f), \
        dtype=real_same_precision_as(psd))

    if low_frequency_cutoff:
        kmin = int(low_frequency_cutoff / psd.delta_f)
        inv_asd[0:kmin] = 0

    ifft(inv_asd, q)

    trunc_start = max_filter_len // 2
    trunc_end = N - max_filter_len // 2
    if trunc_end < trunc_start:
        raise ValueError('Invalid value in inverse_spectrum_truncation')

    if trunc_method == 'hann':
        trunc_window = Array(numpy.hanning(max_filter_len), dtype=q.dtype)
        q[0:trunc_start] *= trunc_window[max_filter_len//2:max_filter_len]
        q[trunc_end:N] *= trunc_window[0:max_filter_len//2]

    if trunc_start < trunc_end:
        q[trunc_start:trunc_end] = 0
    psd_trunc = FrequencySeries(numpy.zeros(len(psd)), delta_f=psd.delta_f, \
                                dtype=complex_same_precision_as(psd))
    fft(q, psd_trunc)
    psd_trunc *= psd_trunc.conj()
    psd_out = 1. / abs(psd_trunc)

    return psd_out