scipy.signal.windows.lanczos

scipy.signal.windows.lanczos(M, *, sym=True)

Return a Lanczos window also known as a sinc window.

Parameters:

Mint

Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative.

symbool, optional

When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.

Returns:

wndarray

The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).

Notes

The Lanczos window is defined as

\[w(n) = sinc \left( \frac{2n}{M - 1} - 1 \right)\]

where

\[sinc(x) = \frac{\sin(\pi x)}{\pi x}\]

The Lanczos window has reduced Gibbs oscillations and is widely used for filtering climate timeseries with good properties in the physical and spectral domains.

Added in version 1.10.

References

[1]

Lanczos, C., and Teichmann, T. (1957). Applied analysis. Physics Today, 10, 44.

[2]

Duchon C. E. (1979) Lanczos Filtering in One and Two Dimensions. Journal of Applied Meteorology, Vol 18, pp 1016-1022.

[3]

Thomson, R. E. and Emery, W. J. (2014) Data Analysis Methods in Physical Oceanography (Third Edition), Elsevier, pp 593-637.

[4]

Wikipedia, “Window function”, http://en.wikipedia.org/wiki/Window_function

Examples

Try it in your browser!

Plot the window

>>> import numpy as np
>>> from scipy.signal.windows import lanczos
>>> from scipy.fft import fft, fftshift
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1)
>>> window = lanczos(51)
>>> ax.plot(window)
>>> ax.set_title("Lanczos window")
>>> ax.set_ylabel("Amplitude")
>>> ax.set_xlabel("Sample")
>>> fig.tight_layout()
>>> plt.show()

and its frequency response:

>>> fig, ax = plt.subplots(1)
>>> A = fft(window, 2048) / (len(window)/2.0)
>>> freq = np.linspace(-0.5, 0.5, len(A))
>>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
>>> ax.plot(freq, response)
>>> ax.set_xlim(-0.5, 0.5)
>>> ax.set_ylim(-120, 0)
>>> ax.set_title("Frequency response of the lanczos window")
>>> ax.set_ylabel("Normalized magnitude [dB]")
>>> ax.set_xlabel("Normalized frequency [cycles per sample]")
>>> fig.tight_layout()
>>> plt.show()

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