# cupyx.scipy.signal.windows.tukey#

cupyx.scipy.signal.windows.tukey(M, alpha=0.5, sym=True)[source]#

Return a Tukey window, also known as a tapered cosine window.

Parameters
• M (int) – Number of points in the output window. If zero or less, an empty array is returned.

• alpha (float, optional) – Shape parameter of the Tukey window, representing the fraction of the window inside the cosine tapered region. If zero, the Tukey window is equivalent to a rectangular window. If one, the Tukey window is equivalent to a Hann window.

• sym (bool, 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

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

Return type

ndarray

Notes

References

1

Harris, Fredric J. (Jan 1978). “On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform”. Proceedings of the IEEE 66 (1): 51-83. 10.1109/PROC.1978.10837

2

Wikipedia, “Window function”, https://en.wikipedia.org/wiki/Window_function#Tukey_window

Examples

Plot the window and its frequency response:

```>>> import cupyx.scipy.signal.windows
>>> import cupy as cp
>>> from cupy.fft import fft, fftshift
>>> import matplotlib.pyplot as plt
```
```>>> window = cupyx.scipy.signal.windows.tukey(51)
>>> plt.plot(cupy.asnumpy(window))
>>> plt.title("Tukey window")
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")
>>> plt.ylim([0, 1.1])
```
```>>> plt.figure()
>>> A = fft(window, 2048) / (len(window)/2.0)
>>> freq = cupy.linspace(-0.5, 0.5, len(A))
>>> response = 20 * cupy.log10(cupy.abs(fftshift(A / cupy.abs(A).max())))
>>> plt.plot(cupy.asnumpy(freq), cupy.asnumpy(response))
>>> plt.axis([-0.5, 0.5, -120, 0])
>>> plt.title("Frequency response of the Tukey window")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")
```