def calc_spectrum(signal, rate):
    """Return the spectrum and frequency indexes for real-valued input signal"""
    npts = len(signal)
    padto = 1 << (npts - 1).bit_length()
    # print 'length of signal {}, pad to {}'.format(npts, padto)
    npts = padto

    sp = np.fft.rfft(signal, n=padto) / npts
    # print('sp len ', len(sp))
    freq = np.arange((npts / 2) + 1) / (npts / rate)
    # print('freq len ', len(freq))
    return freq, abs(sp)