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komm.LloydMaxQuantizer

Lloyd–Max scalar quantizer. It is a scalar quantizer that minimizes the mean-squared error (MSE) between the input signal $X$ and its quantized version. For more details, see Say06, Sec. 9.6.1.

Parameters:

  • input_pdf (Callable[[NDArray[floating]], NDArray[floating]]) –

    The probability density function $f_X(x)$ of the input signal.

  • input_range (tuple[float, float]) –

    The range $(x_\mathrm{min}, x_\mathrm{max})$ of the input signal.

  • num_levels (int) –

    The number $L$ of quantization levels. It must be greater than $1$.

Examples:

>>> uniform_pdf = lambda x: 1/8 * (np.abs(x) <= 4)
>>> quantizer = komm.LloydMaxQuantizer(input_pdf=uniform_pdf, input_range=(-4, 4), num_levels=8)
>>> quantizer.levels
array([-3.5, -2.5, -1.5, -0.5,  0.5,  1.5,  2.5,  3.5])
>>> quantizer.thresholds
array([-3., -2., -1.,  0.,  1.,  2.,  3.])

>>> gaussian_pdf = lambda x: 1/np.sqrt(2*np.pi) * np.exp(-x**2/2)
>>> quantizer = komm.LloydMaxQuantizer(input_pdf=gaussian_pdf, input_range=(-5, 5), num_levels=8)
>>> quantizer.levels.round(3)
array([-2.152, -1.344, -0.756, -0.245,  0.245,  0.756,  1.344,  2.152])
>>> quantizer.thresholds.round(3)
array([-1.748, -1.05 , -0.501, -0.   ,  0.501,  1.05 ,  1.748])

levels: npt.NDArray[np.floating] property

The quantizer levels $v_0, v_1, \ldots, v_{L-1}$.

Examples:

>>> gaussian_pdf = lambda x: 1/np.sqrt(2*np.pi) * np.exp(-x**2/2)
>>> quantizer = komm.LloydMaxQuantizer(input_pdf=gaussian_pdf, input_range=(-5, 5), num_levels=8)
>>> quantizer.levels.round(3)
array([-2.152, -1.344, -0.756, -0.245,  0.245,  0.756,  1.344,  2.152])

thresholds: npt.NDArray[np.floating] property

The quantizer finite thresholds $t_1, t_2, \ldots, t_{L-1}$.

Examples:

>>> gaussian_pdf = lambda x: 1/np.sqrt(2*np.pi) * np.exp(-x**2/2)
>>> quantizer = komm.LloydMaxQuantizer(input_pdf=gaussian_pdf, input_range=(-5, 5), num_levels=8)
>>> quantizer.thresholds.round(3)
array([-1.748, -1.05 , -0.501, -0.   ,  0.501,  1.05 ,  1.748])

__call__

Quantizes the input signal.

Parameters:

  • input (ArrayLike) –

    The input signal $x$ to be quantized.

Returns:

  • output (NDArray[floating]) –

    The quantized signal $y$.

Examples:

>>> gaussian_pdf = lambda x: 1/np.sqrt(2*np.pi) * np.exp(-x**2/2)
>>> quantizer = komm.LloydMaxQuantizer(input_pdf=gaussian_pdf, input_range=(-5, 5), num_levels=8)
>>> quantizer([0, 1, 2, 3, 4, 5, 6, 7]).round(3)
array([0.245, 0.756, 2.152, 2.152, 2.152, 2.152, 2.152, 2.152])