numpy.blackman¶

numpy.blackman(M)[source]¶

Return the Blackman window.

The Blackman window is a taper formed by using the first threeterms of a summation of cosines. It was designed to have close to theminimal leakage possible. It is close to optimal, only slightly worsethan a Kaiser window.

Parameters:	M:int Number of points in the output window. If zero or less, an emptyarray is returned.
Returns:	out:ndarray The window, with the maximum value normalized to one (the value oneappears only if the number of samples is odd).

See also

bartlett,hamming,hanning,kaiser

Notes

The Blackman window is defined as

w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)

Most references to the Blackman window come from the signal processingliterature, where it is used as one of many windowing functions forsmoothing values. It is also known as an apodization (which means“removing the foot”, i.e. smoothing discontinuities at the beginningand end of the sampled signal) or tapering function. It is known as a“near optimal” tapering function, almost as good (by some measures)as the kaiser window.

References

Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,Dover Publications, New York.

Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.

Examples

>>>np.blackman(12)array([ -1.38777878e-17,   3.26064346e-02,   1.59903635e-01,         4.14397981e-01,   7.36045180e-01,   9.67046769e-01,         9.67046769e-01,   7.36045180e-01,   4.14397981e-01,         1.59903635e-01,   3.26064346e-02,  -1.38777878e-17])

Plot the window and the frequency response:

>>>fromnumpy.fftimportfft,fftshift>>>window=np.blackman(51)>>>plt.plot(window)[<matplotlib.lines.Line2D object at 0x...>]>>>plt.title("Blackman window")<matplotlib.text.Text object at 0x...>>>>plt.ylabel("Amplitude")<matplotlib.text.Text object at 0x...>>>>plt.xlabel("Sample")<matplotlib.text.Text object at 0x...>>>>plt.show()

>>>plt.figure()<matplotlib.figure.Figure object at 0x...>>>>A=fft(window,2048)/25.5>>>mag=np.abs(fftshift(A))>>>freq=np.linspace(-0.5,0.5,len(A))>>>response=20*np.log10(mag)>>>response=np.clip(response,-100,100)>>>plt.plot(freq,response)[<matplotlib.lines.Line2D object at 0x...>]>>>plt.title("Frequency response of Blackman window")<matplotlib.text.Text object at 0x...>>>>plt.ylabel("Magnitude [dB]")<matplotlib.text.Text object at 0x...>>>>plt.xlabel("Normalized frequency [cycles per sample]")<matplotlib.text.Text object at 0x...>>>>plt.axis('tight')(-0.5, 0.5, -100.0, ...)>>>plt.show()