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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 wigner_ville_spectrum(data, delta, time_bandwidth=3.5, number_of_tapers=None, smoothing_filter=None, filter_width=100, frequency_divider=1, verbose=False):
 """ Function to calculate the Wigner-Ville Distribution or Wigner-Ville Spectrum of a signal using multitaper spectral estimates. In general it gives better temporal and frequency resolution than a spectrogram but introduces many artifacts and possibly negative values which are not physical. This can be alleviated a bit by applying a smoothing kernel which is also known as a reduced interference distribution (RID). Wraps the ``wv_spec()`` and ``wv_spec_to_array()`` subroutines of the Fortran library. It is very slow for large arrays so try with a small one (< 5000 samples) first. :param data: The input signal. :type data: numpy.ndarray :param delta: The sampling interval of the data. :type delta: float :param time_bandwidth: Time bandwidth product for the tapers. :type time_bandwidth: float :param number_of_tapers: Number of tapers to use. If ``None``, the number will be automatically determined from the time bandwidth product which is usually the optimal choice. :type number_of_tapers: int :param smoothing_filter: One of ``"boxcar"``, ``"gauss"`` or just ``None`` :type smoothing_filter: str :param filter_width: Filter width in samples. :type filter_width: int :param frequency_divider: This method will always calculate all adjustment of the maximum frequency, so that the frequencies range from 0 .. Nyquist frequency / int(frequency_divider). :type frequency_divider: int :param verbose: Verbose output on/off. :type verbose: bool .. rubric:: Example This example demonstrates how to plot a signal, its multitaper spectral estimate, and its Wigner-Ville time-frequency distribution. The signal is sinusoidal overlaid with two simple linear chirps. Get the example signal. Plot the data on the top axes. Plot its spectral estimate on the side. Create and plot the Wigner-Ville distribution. .. plot:: # Same as the above code snippet just a bit prettier. import matplotlib.pyplot as plt plt.style.use("ggplot") from mtspec import mtspec, wigner_ville_spectrum from mtspec.util import signal_bursts import numpy as np fig = plt.figure() data = signal_bursts() # Plot the data ax1 = fig.add_axes([0.2,0.75, 0.79, 0.23]) ax1.plot(data, color="0.1") ax1.set_xlim(0, len(data)) # Plot multitaper spectrum ax2 = fig.add_axes([0.06,0.02,0.13,0.69]) spec, freq = mtspec(data, 10, 3.5) ax2.plot(spec, freq, color="0.1") ax2.set_xlim(0, spec.max()) ax2.set_ylim(freq[0], freq[-1]) ax2.set_xticks([]) # Create the wigner ville spectrum wv = wigner_ville_spectrum(data, 10, 3.5, smoothing_filter='gauss') # Plot the WV ax3 = fig.add_axes([0.2, 0.02, 0.79, 0.69]) ax3.set_yticks([]) ax3.set_xticks([]) ax3.imshow(np.sqrt(abs(wv)), interpolation='lanczos', aspect='auto', cmap="magma") """

    data = np.require(data, 'float32')
    mt = _MtspecType("float32")

    npts = len(data)

    # Use the optimal number of tapers in case no number is specified.
    if number_of_tapers is None:
        number_of_tapers = int(2 * time_bandwidth) - 1

    # Determine filter.
    if not smoothing_filter:
        smoothing_filter = 0
    elif smoothing_filter == 'boxcar':
        smoothing_filter = 1
    elif smoothing_filter == 'gauss':
        smoothing_filter = 2
    else:
        msg = 'Invalid value for smoothing filter.'
        raise Exception(msg)

    # Verbose mode on or off.
    if verbose:
        verbose = C.byref(C.c_char('y'))
    else:
        verbose = None

    # Allocate the output array
    # f90 code internally pads zeros to 2 * npts. That is we only return
    # every second frequency point, thus decrease the size of the array
    output = mt.empty((npts // 2 // int(frequency_divider) + 1, npts))

    mtspeclib.wv_spec_to_array_(C.byref(C.c_int(npts)),
                                C.byref(C.c_float(delta)),
                                mt.p(data), mt.p(output),
                                C.byref(C.c_float(time_bandwidth)),
                                C.byref(C.c_int(number_of_tapers)),
                                C.byref(C.c_int(smoothing_filter)),
                                C.byref(C.c_float(filter_width)),
                                C.byref(C.c_int(frequency_divider)), verbose)

    return output