cupyx.scipy.signal.windows.general_cosine#
- cupyx.scipy.signal.windows.general_cosine(M, a, sym=True)[source]#
Generic weighted sum of cosine terms window
- Parameters:
M (int) – Number of points in the output window
a (array_like) – Sequence of weighting coefficients. This uses the convention of being centered on the origin, so these will typically all be positive numbers, not alternating sign.
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.
Notes
For more information, see [1] and [2]
References
Examples
Heinzel describes a flat-top window named “HFT90D” with formula: [2]
\[w_j = 1 - 1.942604 \cos(z) + 1.340318 \cos(2z) - 0.440811 \cos(3z) + 0.043097 \cos(4z)\]where
\[z = \frac{2 \pi j}{N}, j = 0...N - 1\]Since this uses the convention of starting at the origin, to reproduce the window, we need to convert every other coefficient to a positive number:
>>> HFT90D = [1, 1.942604, 1.340318, 0.440811, 0.043097]
The paper states that the highest sidelobe is at -90.2 dB. Reproduce Figure 42 by plotting the window and its frequency response, and confirm the sidelobe level in red:
>>> from cupyx.scipy.signal.windows import general_cosine >>> from cupy.fft import fft, fftshift >>> import cupy >>> import matplotlib.pyplot as plt
>>> window = general_cosine(1000, HFT90D, sym=False) >>> plt.plot(cupy.asnumpy(window)) >>> plt.title("HFT90D window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample")
>>> plt.figure() >>> A = fft(window, 10000) / (len(window)/2.0) >>> freq = cupy.linspace(-0.5, 0.5, len(A)) >>> response = cupy.abs(fftshift(A / cupy.abs(A).max())) >>> response = 20 * cupy.log10(cupy.maximum(response, 1e-10)) >>> plt.plot(cupy.asnumpy(freq), cupy.asnumpy(response)) >>> plt.axis([-50/1000, 50/1000, -140, 0]) >>> plt.title("Frequency response of the HFT90D window") >>> plt.ylabel("Normalized magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axhline(-90.2, color='red') >>> plt.show()