Added an example of Lanczos weights

lanczos_wgts.py

+""" Draw a set of Lanczos Weights based on
+https://scitools.org.uk/iris/docs/v1.2/examples/graphics/SOI_filtering.html
+"""
+
+__author__ = "Carl Schreck"
+__email__ = "cjschrec@ncsu.edu"
+__copyright__ = "Copyright 2020, North Carolina State University"
+__license__ = "BSD-3.0"
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+def low_pass_weights(window, cutoff):
+    """Calculate weights for a low pass Lanczos filter.
+
+    Args:
+
+    window: int
+        The length of the filter window.
+
+    cutoff: float
+        The cutoff frequency in inverse time steps.
+
+    """
+    order = ((window - 1) // 2 ) + 1
+    nwts = 2 * order + 1
+    w = np.zeros([nwts])
+    n = nwts // 2
+    w[n] = 2 * cutoff
+    k = np.arange(1., n)
+    sigma = np.sin(np.pi * k / n) * n / (np.pi * k)
+    firstfactor = np.sin(2. * np.pi * cutoff * k) / (np.pi * k)
+    w[n-1:0:-1] = firstfactor * sigma
+    w[n+1:-1] = firstfactor * sigma
+    return w[1:-1]
+
+y = low_pass_weights(window=41, cutoff=0.10)
+x = np.arange(-20,21)
+plt.plot(x, y)
+plt.savefig('figures/lanczos_wgts.png')
+plt.show()