diff options
Diffstat (limited to 'numpy/lib/function_base.py')
| -rw-r--r-- | numpy/lib/function_base.py | 98 |
1 files changed, 94 insertions, 4 deletions
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py index 8aed772d1..4236ca1bb 100644 --- a/numpy/lib/function_base.py +++ b/numpy/lib/function_base.py @@ -809,7 +809,16 @@ def interp(x, xp, fp, left=None, right=None): def angle(z, deg=0): - """Return the angle of the complex argument z. + """ + Return the angle of the complex argument z. + + Examples + -------- + >>> numpy.angle(1+1j) # in radians + 0.78539816339744828 + >>> numpy.angle(1+1j,deg=True) # in degrees + 45.0 + """ if deg: fact = 180/pi @@ -889,11 +898,12 @@ if sys.hexversion < 0x2040000: from sets import Set as set def unique(x): - """Return sorted unique items from an array or sequence. + """ + Return sorted unique items from an array or sequence. Examples -------- - >>> unique([5,2,4,0,4,4,2,2,1]) + >>> numpy.unique([5,2,4,0,4,4,2,2,1]) array([0, 1, 2, 4, 5]) """ @@ -1187,7 +1197,87 @@ def blackman(M): return 0.42-0.5*cos(2.0*pi*n/(M-1)) + 0.08*cos(4.0*pi*n/(M-1)) def bartlett(M): - """bartlett(M) returns the M-point Bartlett window. + """ + Return the Bartlett window. + + The Bartlett window is very similar to a triangular window, except + that the end points are at zero. It is often used in signal + processing for tapering a signal, without generating too much + ripple in the frequency domain. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an + empty array is returned. + + Returns + ------- + out : array + The triangular window, normalized to one (the value one + appears only if the number of samples is odd), with the first + and last samples equal to zero. + + See Also + -------- + blackman, hamming, hanning, kaiser + + Notes + ----- + The Bartlett window is defined as + + .. math:: w(n) = \frac{2}{M-1} (\frac{M-1}{2} - |n - \frac{M-1}{2}|) + + Most references to the Bartlett window come from the signal + processing literature, where it is used as one of many windowing + functions for smoothing values. Note that convolution with this + window produces linear interpolation. It is also known as an + apodization (which means"removing the foot", i.e. smoothing + discontinuities at the beginning and end of the sampled signal) or + tapering function. + + References + ---------- + .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", + Biometrika 37, 1-16, 1950. + .. [2] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal + Processing", Prentice-Hall, 1999, pp. 468-471. + .. [3] Wikipedia, "Window function", + http://en.wikipedia.org/wiki/Window_function + .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, + "Numerical Recipes", Cambridge University Press, 1986, page 429. + + Examples + -------- + >>> from numpy import bartlett + >>> bartlett(12) + array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, + 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636, + 0.18181818, 0. ]) + + # Plot the window and the frequency response of it. + >>> from numpy import clip, log10, array, bartlett + >>> from scipy.fftpack import fft + >>> from matplotlib import pyplot as plt + + >>> window = bartlett(51) + >>> plt.plot(window) + >>> plt.title("Bartlett window") + >>> plt.ylabel("Amplitude") + >>> plt.xlabel("Sample") + >>> plt.show() + + >>> A = fft(window, 2048) / 25.5 + >>> mag = abs(fftshift(A)) + >>> freq = linspace(-0.5,0.5,len(A)) + >>> response = 20*log10(mag) + >>> response = clip(response,-100,100) + >>> plt.plot(freq, response) + >>> plt.title("Frequency response of Bartlett window") + >>> plt.ylabel("Magnitude [dB]") + >>> plt.xlabel("Normalized frequency [cycles per sample]") + >>> plt.axis('tight'); plt.show() + """ if M < 1: return array([]) |