def check_random_odd(self):
for n in [33,65,55]:
f=random ((n,))
af=sum(f,axis=0)/n
f=f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(ihilbert(hilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
def check_definition(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = hilbert(sin(x))
y1 = direct_hilbert(sin(x))
assert_array_almost_equal (y,y1)
assert_array_almost_equal(hilbert(sin(2*x)),
direct_hilbert(sin(2*x)))
def bench_random(self,level=5):
print
print ' Hilbert transform of periodic functions'
print '========================================='
print ' size | optimized | naive'
print '-----------------------------------------'
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print '%6s' % size,
sys.stdout.flush()
x = arange (size)*2*pi/size
if size<2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
else:
f = sin(x)*cos(4*x)
assert_array_almost_equal(hilbert(f),direct_hilbert(f))
print '| %9.2f' % self.measure('hilbert(f)',repeat),
sys.stdout.flush()
print '| %9.2f' % self.measure('direct_hilbert(f)',repeat),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
def check_tilbert_relation(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
f = sin (x)+cos (2*x)*sin(x)
y = hilbert(f)
y1 = direct_hilbert(f)
assert_array_almost_equal (y,y1)
y2 = tilbert(f,h=10)
assert_array_almost_equal (y,y2)
def check_random_even(self):
for n in [32,64,56]:
f=random ((n,))
af=sum(f,axis=0)/n
f=f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(direct_hilbert(direct_ihilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)