def firebp(n, w1, w2, Del):
"""[h,rs,be] = firebp(n,w1,w2,Del);
Bandpass linear phase FIR filter design with specified ripple sizes.
- the derivative of the frequency response amplitude at w1 is
set equal to the negative derivative of the amplitude at w2 -
author : Ivan Selesnick, Rice University, Dec 94
parameters
h : filter of length 2*n+1
rs : reference set upon convergence
be : band edges of h
w1 : first half-magnitude frequency
w2 : second half-magnitude frequency
w1 < w2, w1,w2 should be in the interval (0,pi)
Del : [ripple size in first stopband, passband, second stopband]
subprograms needed
localmax, frefine, firfbe
EXAMPLE
n = 23;
w1 = 0.14 * 2*pi;
w2 = 0.34 * 2*pi;
Del = [0.01 0.03 0.01];
[h,rs,be] = firebp(n,w1,w2,Del);
"""
def rem(a, b):
return a % b
try:
log2
except:
def log2(a):
return log(a, 2)
def mp(t, lngth): #minus_plus vector [-1 1 -1 ... (-1)^lngth]
assert isinstance(lngth,
int), 'Length argument to mp must be an integer. '
assert isinstance(t,str) and t in ['vview_d','vview_f'],\
"type argument must be 'vview_d' or 'vview_f'"
retview = create(t, lngth).fill(1.0)
retview[:lngth:2].fill(-1.0)
return retview
def diff(a):
assert 'pyJvsip' in repr(a), 'diff only works with pyJvsip views'
assert 'vview' in a.type, 'diff only works with vector views'
if a.length > 1:
retview = a[1:a.length] - a[:a.length - 1]
return retview
else:
return None
def srmp(t, s, e):
assert isinstance(e, int) and isinstance(
s, int), 'start and end must be intergers'
assert e > s, 'simple ramps alwasy go up; end > start '
return pv.create(t, e - s + 1).ramp(s, 1)
def coscoef(rs, n, V, Y):
f = {'vview_d': 'mview_d', 'vview_f': 'mview_f'}
m = rs.length + 1
y = pv.create(Y.type, m)
y[:Y.length] = Y
y[m - 1] = 0.0
A = pv.create(f[y.type], m, y.length)
a = A[:rs.length, :n + 1]
a = pv.outer(1, rs, pv.create(rs.type, n + 1).ramp(0, 1), a).cos
at = A.rowview(m - 1)
A.rowview(m - 1)[:] = V[:]
return A.luSolve(y)
# ------------------ initialize constants ---------------------------
assert 'pyJvsip' in repr(Del) and Del.type in ['vview_f','vview_d'],\
"last argument is a vector view of type 'vview_f' or 'vview_d'"
t = Del.type
L = int(pow(2, int(ceil(log2(10 * n)))))
w = pv.create(t, L + 1).ramp(0, pi / float(L)) # frequency axis
N = n - 2 # number of _non-specified interpolation points
SN = 1e-8 # Small Number (stopping criterion)
H0 = pv.create(t, 2 * (L + 1 - n) + 2 * n - 2).fill(0.0)
V = pv.create(t, n + 1).ramp(0, 1)
V *= V.empty.ramp(0, w1).sin + V.empty.ramp(0, w2).sin
ideal = Del.empty.fill(0.0)
ideal[1] = 1.0
up = ideal + Del
lo = ideal - Del
D1 = 0.5 # half-magnitude value at w1
D2 = 0.5 # half-magnitude value at w2
PF = False # PF : flag : Plot Figures
# ------------------ initialize reference set ----------------------------
# n1 : number of reference frequencies in first stopband
# n2 : number of reference frequencies in passband
# n3 : number of reference frequencies in second stopband
n2 = int(round(N * (w2 - w1) / pi))
if rem(n2, 2) == 0:
n2 = n2 - 1
n1 = int(floor((N - n2) * w1 / (pi - (w2 - w1))))
n3 = N - n2 - n1
rs = pv.create(t, n1 + n2 + n3 + 2)
R1 = rs[0:n1].ramp(0, 1)
R1 *= w1 / float(n1)
R2 = rs[n1 + 1:n1 + 1 + n2].ramp(1, 1)
R2 *= (w2 - w1) / float(n2 + 1)
R2 += w1
R3 = rs[n1 + n2 + 2:n1 + n2 + 2 + n3].ramp(1, 1)
R3 *= (pi - w2) / float(n3)
R3 += w2
rs[n1] = w1
rs[n1 + 1 + n2] = w2
# ------------------ initialize interpolation values ---------------------
Y = pv.create(t, n1 + n2 + n3 + 2).fill(0.0)
if n1 % 2 == 0:
Y[0:n1:2].fill(up[0])
Y[1:n1:2].fill(lo[0])
else:
Y[0:n1:2].fill(lo[0])
Y[1:n1:2].fill(up[0])
Y[n1] = D1
o = n1 + 1
l = n1 + 1 + n2
Y[o:l:2].fill(up[1])
Y[o + 1:l:2].fill(lo[1])
Y[l] = D2
o = l + 1
l = o + n3
Y[o:l:2].fill(lo[2])
Y[o + 1:l:2].fill(up[2])
# begin looping
Err = 1
while Err > SN:
# --------------- calculate cosine coefficients -----------------------
a = coscoef(rs, n, V, Y)
# --------------- calculate frequency response ------------------------
#H = real(fft([a(1);a(2:n+1)/2;Z;a(n+1:-1:2)/2])); H = H(1:L+1);
attr = a.attrib
ot = attr['offset']
lt = attr['length']
st = attr['stride']
ot += (lt - 1) * st
st = -st
attr['offset'] = ot
attr['stride'] = st
a_rev = a.cloneview
a_rev.putattrib(attr)
H0.fill(0.0)
H0[0] = a[0]
H0[1:lt] = a[1:] * 0.5
H0[H0.length - n:] = a_rev[:lt - 1] * 0.5
Hc = H0.rcfft
H = Hc.realview[:L + 1].copy
# --------------- determine local max and min -------------------------
v1 = localmax(H)
v2 = localmax(H.copy.neg)
if v1[0] < v2[0]:
s = 0
else:
s = 1
#ri = sortip([v1; v2]);
ri = pv.create(H.type, v1.length + v2.length)
ri[:v1.length] = v1
ri[v1.length:] = v2
ri.sortip()
rs = (ri) * (pi / L)
rs = frefine(a, rs)
n1 = rs.llt(w1).sumval
n2 = pv.bb_and(rs.lgt(w1), rs.llt(w2),
pv.create('vview_bl', rs.length)).sumval
n3 = rs.lgt(w2).sumval
# --------------- calculate frequency response at local max and min ---
Hr = rs.outer(srmp(rs.type, 0, n)).cos.prod(a)
Id = pv.create(Del.type, n1 + n2 + n3)
Dr = Id.empty
Id[:n1].fill(ideal[0])
Id[n1:n1 + n2].fill(ideal[1])
Id[n1 + n2:].fill(ideal[2])
Dr[:n1].fill(Del[0])
Dr[n1:n1 + n2].fill(Del[1])
Dr[n1 + n2:].fill(Del[2])
Er = (Hr - Id) * Dr.recip
# Plot Figures if PF is True
if PF:
figure(1)
plot((w * (1. / pi)).list, H.list)
hold(True)
plot((rs * (1.0 / pi)).list, Hr.list, 'o')
hold(False)
axis([0, 1, -.2, 1.2])
figure(2)
plot(Er.list)
hold(True)
plot(Er.list, 'o'),
hold(False)
pause(0.05)
# --------------- calculate new interpolation points -----------------
Y = Id.empty
if n1 % 2 == 0:
Y[0:n1:2].fill(up[0])
Y[1:n1:2].fill(lo[0])
else:
Y[0:n1:2].fill(lo[0])
Y[1:n1:2].fill(up[0])
Y[n1 + 1:n1 + n2:2].fill(lo[1])
Y[n1:n1 + n2:2].fill(up[1])
Y[n1 + n2 + 1::2].fill(up[2])
Y[n1 + n2::2].fill(lo[2])
# --------------- slim down the set of local max and min --------------
# --------------- to obtain new reference set of correct size ---------
if (rs.length - N) == 1: # remove one frequency from the reference set
if abs(Er[0] - Er[1]) < abs(Er[rs.length - 1] - Er[rs.length - 2]):
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
elif (rs.length - N) == 2: # remove two frequencies
# remove either the two endpoints or remove two adjacent points in the ref. set
k = (diff(Er) * (mp(Er.type, rs.length - 1) + s)).minvalindex + 1
if (k == 1) | (k == (rs.length - 1)):
if k == 1:
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
if abs(Er[0] - Er[1]) < abs(Er[rs.length - 1] -
Er[rs.length - 2]):
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
else:
I = k
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
elif (rs.length - N) == 3: # remove three frequencies
# just use the code for (rs.length-N)==1, followed by the code for (rs.length-N)==2
if abs(Er[0] - Er[1]) < abs(Er[rs.length - 1] - Er[rs.length - 2]):
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
k = (diff(Er) * (mp(Er.type, rs.length - 1) + s)).minvalindex + 1
if (k == 1) or (k == (rs.length - 1)):
if k == 1:
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
if abs(Er[0] - Er[1]) < abs(Er[rs.length - 1] -
Er[rs.length - 2]):
I = 1
s = s + 1
else:
I = rs.length
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
else:
I = k
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
del rs[I - 1]
del Y[I - 1]
del Er[I - 1]
# END IF
# calculate error
Err = Er.maxmgval - 1 #max(abs(Er))-1
print(' Err = %20.15f\n' % Err)
if Err > SN:
# --------------- update new interpolation points ---------------------
n1 = rs.llt(w1).sumval
n2 = pv.bb_and(rs.lgt(w1), rs.llt(w2),
pv.create('vview_bl', rs.length)).sumval
n3 = rs.lgt(w2).sumval
Y1 = Y[0:n1].copy
Y2 = Y[n1:n1 + n2].copy
Y3 = Y[n1 + n2:].copy
Y = pv.create(Y1.type, n1 + n2 + n3 + 2)
Y[0:n1] = Y1
Y[n1] = D1
Y[n1 + 1:n1 + n2 + 1] = Y2
Y[n1 + n2 + 1] = D2
Y[n1 + n2 + 2:] = Y3
# --------------- update new reference set ----------------------------
#rs = [rs(1:n1); w1; rs(n1+1:n1+n2); w2; rs(n1+n2+1:n1+n2+n3)]
rst1 = rs[0:n1].copy
rst2 = rs[n1:n1 + n2].copy
rst3 = rs[n1 + n2:].copy
rs = pv.create(rst1.type, rs.length + 2)
rs[:n1] = rst1
rs[n1] = w1
rs[n1 + 1:n1 + n2 + 1] = rst2
rs[n1 + n2 + 1] = w2
rs[n1 + n2 + 2:] = rst3
#end while
# ------------------ calculate band edges ----------------------------
be = firfbe(a, pv.listToJv(Del.type, [w1, w1, w2, w2]),
pv.listToJv(Del.type, [up[0], lo[1], lo[1], up[2]]))
# ------------------ calcuate filter coefficients ----------------------------
#h = [a(n+1:-1:2)/2; a(1); a(2:n+1)/2]
a[1:] *= 0.5
atr = a[1:].attrib
h = pv.create(Del.type, 2 * a.length - 1)
h[a.length - 1] = a[0]
h[a.length:] = a[1:]
atr = a[1:].attrib
atr['offset'] = atr['length']
atr['stride'] *= -1
a.putattrib(atr)
h[:a.length] = a
figure(1)
plot((w * (1.0 / pi)).list, H.list)
hold(True)
plot((rs * (1.0 / pi)).list, Y.list, 'x')
hold(False)
axis([0, 1, -.2, 1.2])
xlabel('w')
ylabel('H')
title('Frequency Response Amplitude')
return (h, rs, be)
def feature2D(img,
Lambda,
w,
masscut=0,
Imin=0,
field=2,
bandpass='******',
verbose=True):
# Written 7-29-03 by Maria Kilfoil
# Finds and measures roughly circular 'features' within an image.
# note: extent should be 2*w+1 in which w is the same as bpass.
# CALLING SEQUENCE:
# f = feature2D(image,lambda,diameter,masscut,Imin,field)
# INPUTS:
# img: (nx,ny) array which presumably contains some features worth finding
# Lambda: length scale of noise to be filtered out, in pixels; typically 1
# w: a parameter which should be a little greater than the radius of the
# largest features in the image.
# Imin: (optional) Set this optional parameter to the minimum allowed value for the peak
# brightness of a feature. Useful for limiting the number of spurious features in
# noisy images. If set to 0 (default), the top 30# of the bright pixels
# will be used.
# masscut: (optional) Setting this parameter saves runtime by reducing the runtime wasted on
# low mass 'noise' features. (default is 0, accept all.)
# field: (optional) Set this parameter to 0 or 1 if image is actually just one (odd or even) field of an interlaced
# (e.g. video) image. All the masks will then be constructed with a 2:1 aspect ratio. Otherwise
# set to 2 for progressive scan cameras.
# bandpass: (optional) Setting this parameter to 'bp' will run feature finding on the bandpassed image, while setting
# it to 'raw' will run feature finding on the raw image. The default is 'raw'.
#
# NOT IMPLEMENTED:
# separation: an optional parameter which specifies the minimum allowable separation
# between feature centers. The default value is diameter+1.
#
#
# OUTPUTS:
# f(:,1): the x centroid positions, in pixels.
# f(:,2): the y centroid positions, in pixels.
# f(:,3): integrated brightness of the features. ("mass")
# f(:,4): the square of the radius of gyration of the features.
# (second moment of the "mass" distribution, where mass=intensity)
# f(:,5): eccentricity, which should be zero for circularly symmetric features and
# order one for very elongated images.
# RESTRICTIONS:
# To work properly, the image must consist of bright, circularly symmetric regions
# on a roughly zero-valued background. To find dark features, the image should be
# inverted and the background subtracted. If the image contains a large amount of
# high spatial frequency noise, performance will be improved by first filtering the image.
# BPASS will remove high spatial frequency noise, and subtract the image background.
# Individual features should NOT overlap.
#
# MODIFICATION HISTORY:
# This code is inspired by feature_stats2 written by
# David G. Grier, U of Chicago, 1992.
# Written by John C. Crocker, U of Chicago, optimizing
# runtime and measurement error, 10/93.
# Matlab version written by Maria L. Kilfoil 2003.
# 10-18-07 Vincent Pelletier, Maria Kilfoil -- added masscut to Matlab version
# June 2013 - Adpated for Python by Kevin Smith (Maria Kilfoil's Group)
extent = 2. * w + 1
if (bandpass == 'bp'):
image = bpass.bpass(img, Lambda, w)
elif (bandpass == 'raw'):
image = img
else:
image = img
if extent % 2 == 0:
print('Requires an odd extent. Adding 1...')
extent = extent + 1
sz = image.shape
nx = sz[1]
ny = sz[0]
# if n_params() eq 2 then sep = extent+1
sep = extent
#Put a border around the image to prevent mask out-of-bounds
#Only use the following 2 lines if you are not using bpass to do spatial filtering first.
#Otherwise, image returned from bpass already had a border of w width
a = image
# Finding the local maxima
loc = localmax.localmax(image, sep, field, Imin)
if len(loc[0]) == 0 or loc[0][0] == -1:
r = -1
return r
x = [0] * len(loc[0])
y = [0] * len(loc[0])
for i in xrange(0, len(loc[0])):
y[i] = int(loc[0][i])
x[i] = int(loc[1][i])
x = x - np.double(0) #convert to arrays
y = y - np.double(0)
nmax = len(loc[0])
m = np.zeros((1, len(loc[0])))[0]
xl = x - (extent // 2)
xh = xl + extent - 1
extent = int(extent)
# Set up some masks
rsq = create_mask.rsqd(extent, extent)
t = create_mask.thetarr(extent)
mask = np.less_equal(rsq, (extent / 2)**2)
mask2 = np.ones((extent, 1)) * np.arange(1, extent + 1, 1) # checked
mask2 = mask2 * mask
mask3 = (rsq * mask) + (1 / 6)
cen = int((extent - 1) / 2)
cmask = np.cos(2 * t) * mask
smask = np.sin(2 * t) * mask
cmask[cen, cen] = 0.0
smask[cen, cen] = 0.0
suba = np.zeros((extent, extent, nmax))
xmask = mask2
ymask = mask2.T
yl = y - (extent // 2)
yh = yl + extent - 1
yscale = 1
ycen = cen
# Estimate the mass
for i in xrange(0, nmax):
m[i] = (np.double(a[int(yl[i]):int(yh[i]) + 1,
int(xl[i]):int(xh[i]) + 1]) * mask).sum()
# remove features based on 'masscut' parameter
b = (m > masscut).nonzero()
nmax = len(b[0])
if nmax == 0:
print('No feature found!')
r = []
return r
xl = xl[b]
xh = xh[b]
yl = yl[b]
yh = yh[b]
x = x[b]
y = y[b]
m = m[b]
if verbose:
print(str(nmax) + ' features found.')
# Setup some result arrays
xc = [0] * nmax - np.double(0)
yc = [0] * nmax - np.double(0)
rg = [0] * nmax - np.double(0)
e = [0] * nmax - np.double(0)
# Calculate feature centers
for i in xrange(0, nmax):
xc[i] = (np.double(a[int(yl[i]):int(yh[i]) + 1,
int(np.fix(xl[i])):int(xh[i]) + 1]) *
xmask).sum()
yc[i] = (np.double(a[int(yl[i]):int(yh[i]) + 1,
int(xl[i]):int(xh[i]) + 1]) * ymask).sum()
x1 = x
y1 = y
# Correct for the 'offset' of the centroid masks
xc = xc / m - ((extent + 1) / 2)
yc = (yc / m - (extent + 1) / 2) / yscale
# Update the positions and correct for the width of the 'border'
x = x + xc - 0 * (extent // 2)
y = (y + yc - 0 * (extent // 2)) * yscale
x2 = x
y2 = y
# Construct the subarray and calculate the mass, squared radius of gyration, eccentricity
for i in xrange(0, nmax):
suba[:, :, i] = fracshift.fracshift(
np.double(a[int(yl[i]):int(yh[i]) + 1,
int(xl[i]):int(xh[i]) + 1]), -xc[i], -yc[i])
m[i] = (suba[:, :, i] * mask).sum()
rg[i] = ((suba[:, :, i] * mask3).sum()) / m[i]
tmp = np.sqrt((((suba[:, :, i] * cmask).sum())**2) +
(((suba[:, :, i] * smask).sum())**2))
tmp2 = (m[i] - suba[cen, ycen, i] + 1e-6)
e[i] = tmp / tmp2
for i in xrange(0, nmax):
xc[i] = np.double(suba[:, :, i] * xmask).sum()
yc[i] = np.double(suba[:, :, i] * ymask).sum()
xc = xc / m - (extent + 1) / 2
yc = (yc / m - (extent + 1) / 2) / yscale # get mass center
x3 = x2 + xc - 0 * (extent // 2)
y3 = (y2 + yc - 0 * (extent // 2)) * yscale
r_mat = np.zeros((nmax, 5))
r_mat[:, 0] = x3 # final x position
r_mat[:, 1] = y3 # final y position
r_mat[:, 2] = m # final integrated intensity
r_mat[:, 3] = rg # final radius of gyration
r_mat[:, 4] = e # final eccentricity
# uncomment the following lines if you would like x1, y1, x2, and x3 to be stored
# (these are the initial position and the position after the first iteration of centroid fitting).
#r2_mat=np.zeros((nmax,4)) #### change to resize array
#r_mat=np.hstack([r_mat,r2_mat])
#r_mat[:,5]=x1
#r_mat[:,6]=y1
#r_mat[:,7]=x2
#r_mat[:,8]=y2
r = r_mat
return r
def firebp(n,w1,w2,Del):
"""[h,rs,be] = firebp(n,w1,w2,Del);
Bandpass linear phase FIR filter design with specified ripple sizes.
- the derivative of the frequency response amplitude at w1 is
set equal to the negative derivative of the amplitude at w2 -
author : Ivan Selesnick, Rice University, Dec 94
parameters
h : filter of length 2*n+1
rs : reference set upon convergence
be : band edges of h
w1 : first half-magnitude frequency
w2 : second half-magnitude frequency
w1 < w2, w1,w2 should be in the interval (0,pi)
Del : [ripple size in first stopband, passband, second stopband]
subprograms needed
localmax, frefine, firfbe
EXAMPLE
n = 23;
w1 = 0.14 * 2*pi;
w2 = 0.34 * 2*pi;
Del = [0.01 0.03 0.01];
[h,rs,be] = firebp(n,w1,w2,Del);
"""
def rem(a,b):
return a % b
try:
log2
except:
def log2(a):
return log(a,2)
def mp(t,lngth): #minus_plus vector [-1 1 -1 ... (-1)^lngth]
assert isinstance(lngth,int),'Length argument to mp must be an integer. '
assert isinstance(t,str) and t in ['vview_d','vview_f'],\
"type argument must be 'vview_d' or 'vview_f'"
retview = create(t,lngth).fill(1.0)
retview[:lngth:2].fill(-1.0)
return retview
def diff(a):
assert 'pyJvsip' in repr(a),'diff only works with pyJvsip views'
assert 'vview' in a.type, 'diff only works with vector views'
if a.length > 1:
retview = a[1:a.length] - a[:a.length - 1]
return retview
else:
return None
def srmp(t,s,e):
assert isinstance(e,int) and isinstance(s,int),'start and end must be intergers'
assert e > s, 'simple ramps alwasy go up; end > start '
return pv.create(t,e-s+1).ramp(s,1)
def coscoef(rs,n,V,Y):
f={'vview_d':'mview_d','vview_f':'mview_f'}
m=rs.length + 1
y=pv.create(Y.type,m)
y[:Y.length]=Y;y[m-1]=0.0
A=pv.create(f[y.type],m,y.length)
a=A[:rs.length,:n+1]
a=pv.outer(1,rs,pv.create(rs.type,n+1).ramp(0,1),a).cos
at=A.rowview(m-1)
A.rowview(m-1)[:]=V[:]
return A.luSolve(y)
# ------------------ initialize constants ---------------------------
assert 'pyJvsip' in repr(Del) and Del.type in ['vview_f','vview_d'],\
"last argument is a vector view of type 'vview_f' or 'vview_d'"
t=Del.type
L = int(pow(2,int(ceil(log2(10*n)))))
w = pv.create(t,L+1).ramp(0,pi/float(L)) # frequency axis
N = n - 2 # number of _non-specified interpolation points
SN = 1e-8 # Small Number (stopping criterion)
H0 = pv.create(t,2*(L+1-n)+2*n-2).fill(0.0)
V = pv.create(t,n+1).ramp(0,1);V *= V.empty.ramp(0,w1).sin + V.empty.ramp(0,w2).sin
ideal = Del.empty.fill(0.0); ideal[1]=1.0
up = ideal + Del
lo = ideal - Del
D1 = 0.5 # half-magnitude value at w1
D2 = 0.5 # half-magnitude value at w2
PF = False # PF : flag : Plot Figures
# ------------------ initialize reference set ----------------------------
# n1 : number of reference frequencies in first stopband
# n2 : number of reference frequencies in passband
# n3 : number of reference frequencies in second stopband
n2 = int(round(N*(w2-w1)/pi))
if rem(n2,2) == 0:
n2 = n2 - 1
n1 = int(floor((N-n2)*w1/(pi-(w2-w1))))
n3 = N-n2-n1
rs = pv.create(t,n1+n2+n3+2)
R1 = rs[0:n1].ramp(0,1); R1 *= w1/float(n1)
R2 = rs[n1+1:n1+1+n2].ramp(1,1);R2 *= (w2-w1)/float(n2+1);R2 += w1
R3 = rs[n1+n2+2:n1+n2+2+n3].ramp(1,1);R3 *= (pi-w2)/float(n3);R3 += w2
rs[n1]=w1; rs[n1+1+n2]=w2
# ------------------ initialize interpolation values ---------------------
Y=pv.create(t,n1+n2+n3+2).fill(0.0)
if n1 % 2 == 0:
Y[0:n1:2].fill(up[0]);Y[1:n1:2].fill(lo[0])
else:
Y[0:n1:2].fill(lo[0]);Y[1:n1:2].fill(up[0])
Y[n1]=D1;o=n1+1;l=n1+1+n2
Y[o:l:2].fill(up[1]);Y[o+1:l:2].fill(lo[1])
Y[l]=D2;o=l+1;l=o+n3
Y[o:l:2].fill(lo[2]);Y[o+1:l:2].fill(up[2])
# begin looping
Err = 1
while Err > SN:
# --------------- calculate cosine coefficients -----------------------
a = coscoef(rs,n,V,Y)
# --------------- calculate frequency response ------------------------
#H = real(fft([a(1);a(2:n+1)/2;Z;a(n+1:-1:2)/2])); H = H(1:L+1);
attr=a.attrib; ot=attr['offset'];lt=attr['length'];st=attr['stride'];
ot+=(lt-1)*st; st=-st;attr['offset']=ot; attr['stride']=st
a_rev=a.cloneview;a_rev.putattrib(attr)
H0.fill(0.0);H0[0]=a[0];H0[1:lt]=a[1:]*0.5; H0[H0.length-n:]=a_rev[:lt-1]*0.5
Hc=H0.rcfft
H=Hc.realview[:L+1].copy
# --------------- determine local max and min -------------------------
v1 = localmax(H)
v2 = localmax(H.copy.neg)
if v1[0] < v2[0]:
s = 0;
else:
s = 1;
#ri = sortip([v1; v2]);
ri=pv.create(H.type,v1.length+v2.length)
ri[:v1.length]=v1;ri[v1.length:]=v2
ri.sortip()
rs = (ri)*(pi/L)
rs = frefine(a,rs)
n1 = rs.llt(w1).sumval
n2 = pv.bb_and(rs.lgt(w1), rs.llt(w2), pv.create('vview_bl',rs.length)).sumval
n3 = rs.lgt(w2).sumval
# --------------- calculate frequency response at local max and min ---
Hr = rs.outer(srmp(rs.type,0,n)).cos.prod(a)
Id=pv.create(Del.type,n1+n2+n3);Dr=Id.empty
Id[:n1].fill(ideal[0]);Id[n1:n1+n2].fill(ideal[1]);Id[n1+n2:].fill(ideal[2])
Dr[:n1].fill(Del[0]);Dr[n1:n1+n2].fill(Del[1]);Dr[n1+n2:].fill(Del[2])
Er = (Hr - Id)*Dr.recip
# Plot Figures if PF is True
if PF:
figure(1)
plot((w*(1./pi)).list,H.list)
hold(True)
plot((rs*(1.0/pi)).list,Hr.list,'o')
hold(False)
axis([0, 1, -.2, 1.2])
figure(2)
plot(Er.list)
hold(True)
plot(Er.list,'o'),
hold(False)
pause(0.05)
# --------------- calculate new interpolation points -----------------
Y=Id.empty
if n1 % 2 == 0:
Y[0:n1:2].fill(up[0]);Y[1:n1:2].fill(lo[0])
else:
Y[0:n1:2].fill(lo[0]);Y[1:n1:2].fill(up[0])
Y[n1+1:n1+n2:2].fill(lo[1]);Y[n1:n1+n2:2].fill(up[1])
Y[n1+n2+1::2].fill(up[2]);Y[n1+n2::2].fill(lo[2])
# --------------- slim down the set of local max and min --------------
# --------------- to obtain new reference set of correct size ---------
if (rs.length-N) == 1: # remove one frequency from the reference set
if abs(Er[0]-Er[1]) < abs(Er[rs.length-1]-Er[rs.length-2]):
I = 1; s = s + 1;
else:
I = rs.length;
del rs[I-1]; del Y[I-1]; del Er[I-1]
elif (rs.length-N) == 2: # remove two frequencies
# remove either the two endpoints or remove two adjacent points in the ref. set
k = (diff(Er)*(mp(Er.type,rs.length-1)+s)).minvalindex+1;
if (k == 1) | (k == (rs.length-1)):
if k == 1:
I = 1; s = s + 1
else:
I = rs.length
del rs[I-1]; del Y[I-1]; del Er[I-1]
if abs(Er[0]-Er[1]) < abs(Er[rs.length-1]-Er[rs.length-2]):
I = 1; s = s + 1;
else:
I = rs.length;
del rs[I-1]; del Y[I-1]; del Er[I-1]
else:
I = k;
del rs[I-1]; del Y[I-1]; del Er[I-1]
del rs[I-1]; del Y[I-1]; del Er[I-1]
elif (rs.length-N) == 3: # remove three frequencies
# just use the code for (rs.length-N)==1, followed by the code for (rs.length-N)==2
if abs(Er[0]-Er[1]) < abs(Er[rs.length-1]-Er[rs.length-2]):
I = 1; s = s + 1
else:
I = rs.length
del rs[I-1]; del Y[I-1]; del Er[I-1]
k = (diff(Er)*(mp(Er.type,rs.length-1)+s)).minvalindex+1
if (k == 1) or (k == (rs.length-1)):
if k == 1:
I = 1; s = s + 1
else:
I = rs.length;
del rs[I-1]; del Y[I-1]; del Er[I-1]
if abs(Er[0]-Er[1]) < abs(Er[rs.length-1]-Er[rs.length-2]):
I = 1; s = s + 1
else:
I = rs.length;
del rs[I-1]; del Y[I-1]; del Er[I-1]
else:
I = k;
del rs[I-1]; del Y[I-1]; del Er[I-1]
del rs[I-1]; del Y[I-1]; del Er[I-1]
# END IF
# calculate error
Err = Er.maxmgval-1 #max(abs(Er))-1
print(' Err = %20.15f\n'%Err)
if Err > SN:
# --------------- update new interpolation points ---------------------
n1 = rs.llt(w1).sumval
n2 = pv.bb_and(rs.lgt(w1), rs.llt(w2), pv.create('vview_bl',rs.length)).sumval
n3 = rs.lgt(w2).sumval
Y1 = Y[0:n1].copy
Y2 = Y[n1:n1+n2].copy
Y3 = Y[n1+n2:].copy
Y = pv.create(Y1.type,n1+n2+n3+2)
Y[0:n1]=Y1;Y[n1]=D1;Y[n1+1:n1+n2+1]=Y2;Y[n1+n2+1]=D2;Y[n1+n2+2:]=Y3
# --------------- update new reference set ----------------------------
#rs = [rs(1:n1); w1; rs(n1+1:n1+n2); w2; rs(n1+n2+1:n1+n2+n3)]
rst1=rs[0:n1].copy;rst2=rs[n1:n1+n2].copy;rst3=rs[n1+n2:].copy
rs=pv.create(rst1.type,rs.length+2)
rs[:n1]=rst1;rs[n1]=w1;rs[n1+1:n1+n2+1]=rst2;rs[n1+n2+1]=w2;rs[n1+n2+2:]=rst3
#end while
# ------------------ calculate band edges ----------------------------
be = firfbe(a,pv.listToJv(Del.type,[w1,w1,w2,w2]),pv.listToJv(Del.type,[up[0],lo[1],lo[1],up[2]]))
# ------------------ calcuate filter coefficients ----------------------------
#h = [a(n+1:-1:2)/2; a(1); a(2:n+1)/2]
a[1:]*=0.5
atr=a[1:].attrib
h=pv.create(Del.type,2*a.length-1)
h[a.length-1]=a[0]
h[a.length:]=a[1:]
atr=a[1:].attrib;atr['offset']=atr['length'];atr['stride']*=-1
a.putattrib(atr);h[:a.length]=a
figure(1); plot((w*(1.0/pi)).list,H.list); hold(True); plot((rs*(1.0/pi)).list,Y.list,'x'); hold(False)
axis([0, 1, -.2, 1.2])
xlabel('w'); ylabel('H'); title('Frequency Response Amplitude')
return(h,rs,be)
data = data[0:9600]
T = len(data)/float(fs)
k = test * T
chunk = 9600
amp, freq = calculatefft(fs, data)
print T
print len(data)
print fs
print k
print np.amax(amp)
print np.where(amp == np.amax(amp))
print freq[np.where(amp == np.amax(amp))]
print localmax(amp, k)
fs, data = read('training330.wav')
for i in range(0, 3):
print "SAMPLES"
print"----------"
tmpdata = data[i*chunk:i*chunk+chunk]
amp, freq = calculatefft(fs, tmpdata)
print k
print np.amax(amp)
print np.where(amp == np.amax(amp))
print freq[np.where(amp == np.amax(amp))]
print localmax(amp, k)
#data = data[0:9600]