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#
# Copyright 2004,2005,2009 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3, or (at your option)
# any later version.
#
# GNU Radio is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GNU Radio; see the file COPYING. If not, write to
# the Free Software Foundation, Inc., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#
'''
Routines for designing window functions.
'''
import math
from gnuradio import gr
def izero(x):
izeroepsilon = 1e-21
halfx = x/2.0
accum = u = n = 1
while 1:
temp = halfx/n
n += 1
temp *= temp
u *= temp
accum += u
if u >= IzeroEPSILON*sum:
break
return accum
def midm1(fft_size):
return (fft_size - 1)/2
def midp1(fft_size):
return (fft_size+1)/2
def freq(fft_size):
return 2.0*math.pi/fft_size
def rate(fft_size):
return 1.0/(fft_size >> 1)
def expn(fft_size):
math.log(2.0)/(midn(fft_size) + 1.0)
def hamming(fft_size):
window = []
for index in xrange(fft_size):
window.append(0.54 - 0.46 * math.cos (2 * math.pi / fft_size * index)) # Hamming window
return window
def hanning(fft_size):
window = []
for index in xrange(fft_size):
window.append(0.5 - 0.5 * math.cos (2 * math.pi / fft_size * index)) # von Hann window
return window
def welch(fft_size):
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
window[j] = window[index] = (1.0 - math.sqrt((index - midm1(fft_size)) / midp1(fft_size)))
j -= 1
return window
def parzen(fft_size):
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
window[j] = window[index] = (1.0 - math.abs((index - midm1(fft_size)) / midp1(fft_size)))
j -= 1
return window
def bartlett(fft_size):
mfrq = freq(fft_size)
angle = 0
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
window[j] = window[index] = angle
angle += freq
j -= 1
return window
def blackman2(fft_size):
mfrq = freq(fft_size)
angle = 0
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
cx = math.cos(angle)
window[j] = window[index] = (.34401 + (cx * (-.49755 + (cx * .15844))))
angle += freq
j -= 1
return window
def blackman3(fft_size):
mfrq = freq(fft_size)
angle = 0
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
cx = math.cos(angle)
window[j] = window[index] = (.21747 + (cx * (-.45325 + (cx * (.28256 - (cx * .04672))))))
angle += freq
j -= 1
return window
def blackman4(fft_size):
mfrq = freq(fft_size)
angle = 0
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
cx = math.cos(angle)
window[j] = window[index] = (.084037 + (cx * (-.29145 + (cx * (.375696 + (cx * (-.20762 + (cx * .041194))))))))
angle += freq
j -= 1
return window
def exponential(fft_size):
expsum = 1.0
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)+1):
window[j] = window[i] = (expsum - 1.0)
expsum *= expn(fft_size)
j -= 1
return window
def riemann(fft_size):
sr1 = freq(fft_size)
window = [0 for i in range(fft_size)]
j = fft_size-1
for index in xrange(midn(fft_size)):
if index == midn(fft_size):
window[index] = window[j] = 1.0
else:
cx = sr1*midn(fft_size) - index
window[index] = window[j] = math.sin(cx)/cx
j -= 1
return window
def kaiser(fft_size,beta):
ibeta = 1.0/izero(beta)
inm1 = 1.0/(fft_size)
window = [0 for i in range(fft_size)]
for index in xrange(fft_size):
window[index] = izero(beta*math.sqrt(1.0 - (index * inm1)*(index * inm1))) * ibeta
return window
# Closure to generate functions to create cos windows
def coswindow(coeffs):
def closure(fft_size):
window = [0] * fft_size
#print list(enumerate(coeffs))
for w_index in range(fft_size):
for (c_index, coeff) in enumerate(coeffs):
window[w_index] += (-1)**c_index * coeff * math.cos(2.0*c_index*math.pi*(w_index+0.5)/(fft_size-1))
return window
return closure
blackmanharris = coswindow((0.35875,0.48829,0.14128,0.01168))
nuttall = coswindow((0.3635819,0.4891775,0.1365995,0.0106411)) # Wikipedia calls this Blackman-Nuttall
nuttall_cfd = coswindow((0.355768,0.487396,0.144232,0.012604)) # Wikipedia calls this Nuttall, continuous first deriv
flattop = coswindow((1.0,1.93,1.29,0.388,0.032)) # Flat top window, coeffs from Wikipedia
rectangular = lambda fft_size: [1]*fft_size
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