Least Lncosh (Llncosh)¶
New in version 1.2.0.
The least lncosh (Llncosh) algorithm (proposed in https://doi.org/10.1016/j.sigpro.2019.107348) is similar to LMS adaptive filter.
The Llncosh filter can be created as follows
>>> import padasip as pa
>>> pa.filters.FilterLlncosh(n)
where n is the size (number of taps) of the filter.
Content of this page:
See also
Algorithm Explanation¶
The lncosh cost function is the natural logarithm of hyperbolic cosine function, which behaves like a hybrid of the mean square error and mean absolute error criteria according to its positive parameter lambd.
Minimal Working Examples¶
If you have measured data you may filter it as follows
import numpy as np
import matplotlib.pylab as plt
import padasip as pa
# creation of data
N = 500
x = np.random.normal(0, 1, (N, 4)) # input matrix
v = np.random.normal(0, 0.1, N) # noise
d = 2 * x[:, 0] + 0.1 * x[:, 1] - 4 * x[:, 2] + 0.5 * x[:, 3] + v # target
# identification
f = pa.filters.FilterLlncosh(n=4, mu=0.1, lambd=0.1, w="random")
y, e, w = f.run(d, x)
# show results
plt.figure(figsize=(15, 9))
plt.subplot(211);
plt.title("Adaptation");
plt.xlabel("samples - k")
plt.plot(d, "b", label="d - target")
plt.plot(y, "g", label="y - output");
plt.legend()
plt.subplot(212);
plt.title("Filter error");
plt.xlabel("samples - k")
plt.plot(10 * np.log10(e ** 2), "r", label="e - error [dB]");
plt.legend()
plt.tight_layout()
plt.show()
