def estimate_beats(audio_path, onset_type, plot=False):
    """Compute beat positions using either a spectral flux or a machine learned onset novelty function,
    followed by computing a tempogram and PLP.

    When onset_type = 'spectral_flux', use librosa.onset.onset strength to compute the novelty function.
    When onset_type = 'machine_learning', use madmom.features.beats.RNNBeatProcessor() to compute the
    novelty function.

    When `plot=True`, plot the onset novelty function and the estimated beats as vertical
    lines on the same plot. Your plot should include all axis labels and the time stamps
    should be in seconds.

    Parameters
    ----------
    audio_path : str
        Path to input audio file
    onset_type : str
        One of 'spectral_flux' or 'machine_learning'
    plot : bool
        If True, plots the onset novelty curve and the estimated beat positions.

    Returns
    -------
    beat_times : 1-d np.array
        Array of time stamps of the estimated beats in seconds.

    """
    # use librosa.onset.onset_strength to compute the spectral flux onset novelty curve
    # use madmom.features.beats.RNNBeatProcessor() to compute the machine learned novelty curve
    # use librosa.beat.plp to compute the PLP function

    #load audio file
    y, sr = librosa.load(audio_path, sr = 22050)

    #SPECTRAL FLUX
    if onset_type == 'spectral_flux':
        onset_env = librosa.onset.onset_strength(y=y, sr=sr)
        #PLP
        pulse = librosa.beat.plp(onset_envelope=onset_env, sr=sr)
        beat_times = np.flatnonzero(librosa.util.localmax(pulse))
        #Time stamps
        times = librosa.times_like(onset_env, sr=sr)
        times_pulse = librosa.times_like(pulse, sr=sr)
        if plot is True:
            ax = plt.subplot(2,1,1)
            plt.plot(times, librosa.util.normalize(onset_env), label='Onset Envelope')
            plt.vlines(times_pulse[beat_times], 0, 1, alpha=0.5, color='r', linestyle='--', label='Estimated Beats [PLP]')
            plt.legend(frameon=True, framealpha=0.75)
            plt.title('SF Onset Envelope')
            plt.xlim(0, 20)
            ax.xaxis.set_major_formatter(librosa.display.TimeFormatter())
            plt.tight_layout()
            plt.show()


    #MACHINE LEARNING
    if onset_type == 'machine_learning':
        proc = madmom.features.beats.RNNBeatProcessor()
        onset_env = proc(audio_path)


        #samplestotime = librosa.core.samples_to_time(onset_env)
        #print("onset_env = ", onset_env)
        #print("len(onset_env) = ", len(onset_env))
        #print("samplestotime = ", samplestotime)
        #print("len(samplestotime) = ", len(samplestotime))


        #PLP
        pulse = librosa.beat.plp(onset_envelope=onset_env, sr=sr)
        beat_times = np.flatnonzero(librosa.util.localmax(pulse))
        #Time stamps
        times = librosa.times_like(onset_env, sr=sr)
        times_pulse = librosa.times_like(pulse, sr=sr)
        if plot is True:
            ax = plt.subplot(2,1,1)
            plt.plot(times, librosa.util.normalize(onset_env), label='Onset Envelope')
            plt.vlines(times_pulse[beat_times], 0, 1, alpha=0.5, color='r', linestyle='--', label='Estimated Beats [PLP]')
            plt.legend(frameon=True, framealpha=0.75)
            plt.title('ML Onset Envelope')
            plt.xlim(0, 20)
            ax.xaxis.set_major_formatter(librosa.display.TimeFormatter())
            plt.tight_layout()
            plt.show()


    #print("beat_times = ", beat_times)
    #print("len(beat_times) = ", len(beat_times))

    return beat_times