import numpy as np
from numpy.testing import (assert_almost_equal, assert_equal,
assert_, assert_allclose, assert_array_equal)
from pytest import raises as assert_raises
import scipy.signal.waveforms as waveforms
# These chirp_* functions are the instantaneous frequencies of the signals
# returned by chirp().
def chirp_linear(t, f0, f1, t1):
f = f0 + (f1 - f0) * t / t1
return f
def chirp_quadratic(t, f0, f1, t1, vertex_zero=True):
if vertex_zero:
f = f0 + (f1 - f0) * t**2 / t1**2
else:
f = f1 - (f1 - f0) * (t1 - t)**2 / t1**2
return f
def chirp_geometric(t, f0, f1, t1):
f = f0 * (f1/f0)**(t/t1)
return f
def chirp_hyperbolic(t, f0, f1, t1):
f = f0*f1*t1 / ((f0 - f1)*t + f1*t1)
return f
def compute_frequency(t, theta):
"""
Compute theta'(t)/(2*pi), where theta'(t) is the derivative of theta(t).
"""
# Assume theta and t are 1-D NumPy arrays.
# Assume that t is uniformly spaced.
dt = t[1] - t[0]
f = np.diff(theta)/(2*np.pi) / dt
tf = 0.5*(t[1:] + t[:-1])
return tf, f
class TestChirp(object):
def test_linear_at_zero(self):
w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='linear')
assert_almost_equal(w, 1.0)
def test_linear_freq_01(self):
method = 'linear'
f0 = 1.0
f1 = 2.0
t1 = 1.0
t = np.linspace(0, t1, 100)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_linear_freq_02(self):
method = 'linear'
f0 = 200.0
f1 = 100.0
t1 = 10.0
t = np.linspace(0, t1, 100)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_quadratic_at_zero(self):
w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic')
assert_almost_equal(w, 1.0)
def test_quadratic_at_zero2(self):
w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic',
vertex_zero=False)
assert_almost_equal(w, 1.0)
def test_quadratic_freq_01(self):
method = 'quadratic'
f0 = 1.0
f1 = 2.0
t1 = 1.0
t = np.linspace(0, t1, 2000)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_quadratic_freq_02(self):
method = 'quadratic'
f0 = 20.0
f1 = 10.0
t1 = 10.0
t = np.linspace(0, t1, 2000)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_logarithmic_at_zero(self):
w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='logarithmic')
assert_almost_equal(w, 1.0)
def test_logarithmic_freq_01(self):
method = 'logarithmic'
f0 = 1.0
f1 = 2.0
t1 = 1.0
t = np.linspace(0, t1, 10000)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_logarithmic_freq_02(self):
method = 'logarithmic'
f0 = 200.0
f1 = 100.0
t1 = 10.0
t = np.linspace(0, t1, 10000)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_logarithmic_freq_03(self):
method = 'logarithmic'
f0 = 100.0
f1 = 100.0
t1 = 10.0
t = np.linspace(0, t1, 10000)
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
assert_(abserr < 1e-6)
def test_hyperbolic_at_zero(self):
w = waveforms.chirp(t=0, f0=10.0, f1=1.0, t1=1.0, method='hyperbolic')
assert_almost_equal(w, 1.0)
def test_hyperbolic_freq_01(self):
method = 'hyperbolic'
t1 = 1.0
t = np.linspace(0, t1, 10000)
# f0 f1
cases = [[10.0, 1.0],
[1.0, 10.0],
[-10.0, -1.0],
[-1.0, -10.0]]
for f0, f1 in cases:
phase = waveforms._chirp_phase(t, f0, t1, f1, method)
tf, f = compute_frequency(t, phase)
expected = chirp_hyperbolic(tf, f0, f1, t1)
assert_allclose(f, expected)
def test_hyperbolic_zero_freq(self):
# f0=0 or f1=0 must raise a ValueError.
method = 'hyperbolic'
t1 = 1.0
t = np.linspace(0, t1, 5)
assert_raises(ValueError, waveforms.chirp, t, 0, t1, 1, method)
assert_raises(ValueError, waveforms.chirp, t, 1, t1, 0, method)
def test_unknown_method(self):
method = "foo"
f0 = 10.0
f1 = 20.0
t1 = 1.0
t = np.linspace(0, t1, 10)
assert_raises(ValueError, waveforms.chirp, t, f0, t1, f1, method)
def test_integer_t1(self):
f0 = 10.0
f1 = 20.0
t = np.linspace(-1, 1, 11)
t1 = 3.0
float_result = waveforms.chirp(t, f0, t1, f1)
t1 = 3
int_result = waveforms.chirp(t, f0, t1, f1)
err_msg = "Integer input 't1=3' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_f0(self):
f1 = 20.0
t1 = 3.0
t = np.linspace(-1, 1, 11)
f0 = 10.0
float_result = waveforms.chirp(t, f0, t1, f1)
f0 = 10
int_result = waveforms.chirp(t, f0, t1, f1)
err_msg = "Integer input 'f0=10' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_f1(self):
f0 = 10.0
t1 = 3.0
t = np.linspace(-1, 1, 11)
f1 = 20.0
float_result = waveforms.chirp(t, f0, t1, f1)
f1 = 20
int_result = waveforms.chirp(t, f0, t1, f1)
err_msg = "Integer input 'f1=20' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_all(self):
f0 = 10
t1 = 3
f1 = 20
t = np.linspace(-1, 1, 11)
float_result = waveforms.chirp(t, float(f0), float(t1), float(f1))
int_result = waveforms.chirp(t, f0, t1, f1)
err_msg = "Integer input 'f0=10, t1=3, f1=20' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
class TestSweepPoly(object):
def test_sweep_poly_quad1(self):
p = np.poly1d([1.0, 0.0, 1.0])
t = np.linspace(0, 3.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = p(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_const(self):
p = np.poly1d(2.0)
t = np.linspace(0, 3.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = p(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_linear(self):
p = np.poly1d([-1.0, 10.0])
t = np.linspace(0, 3.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = p(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_quad2(self):
p = np.poly1d([1.0, 0.0, -2.0])
t = np.linspace(0, 3.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = p(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_cubic(self):
p = np.poly1d([2.0, 1.0, 0.0, -2.0])
t = np.linspace(0, 2.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = p(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_cubic2(self):
"""Use an array of coefficients instead of a poly1d."""
p = np.array([2.0, 1.0, 0.0, -2.0])
t = np.linspace(0, 2.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = np.poly1d(p)(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
def test_sweep_poly_cubic3(self):
"""Use a list of coefficients instead of a poly1d."""
p = [2.0, 1.0, 0.0, -2.0]
t = np.linspace(0, 2.0, 10000)
phase = waveforms._sweep_poly_phase(t, p)
tf, f = compute_frequency(t, phase)
expected = np.poly1d(p)(tf)
abserr = np.max(np.abs(f - expected))
assert_(abserr < 1e-6)
class TestGaussPulse(object):
def test_integer_fc(self):
float_result = waveforms.gausspulse('cutoff', fc=1000.0)
int_result = waveforms.gausspulse('cutoff', fc=1000)
err_msg = "Integer input 'fc=1000' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_bw(self):
float_result = waveforms.gausspulse('cutoff', bw=1.0)
int_result = waveforms.gausspulse('cutoff', bw=1)
err_msg = "Integer input 'bw=1' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_bwr(self):
float_result = waveforms.gausspulse('cutoff', bwr=-6.0)
int_result = waveforms.gausspulse('cutoff', bwr=-6)
err_msg = "Integer input 'bwr=-6' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
def test_integer_tpr(self):
float_result = waveforms.gausspulse('cutoff', tpr=-60.0)
int_result = waveforms.gausspulse('cutoff', tpr=-60)
err_msg = "Integer input 'tpr=-60' gives wrong result"
assert_equal(int_result, float_result, err_msg=err_msg)
class TestUnitImpulse(object):
def test_no_index(self):
assert_array_equal(waveforms.unit_impulse(7), [1, 0, 0, 0, 0, 0, 0])
assert_array_equal(waveforms.unit_impulse((3, 3)),
[[1, 0, 0], [0, 0, 0], [0, 0, 0]])
def test_index(self):
assert_array_equal(waveforms.unit_impulse(10, 3),
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0])
assert_array_equal(waveforms.unit_impulse((3, 3), (1, 1)),
[[0, 0, 0], [0, 1, 0], [0, 0, 0]])
# Broadcasting
imp = waveforms.unit_impulse((4, 4), 2)
assert_array_equal(imp, np.array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 0]]))
def test_mid(self):
assert_array_equal(waveforms.unit_impulse((3, 3), 'mid'),
[[0, 0, 0], [0, 1, 0], [0, 0, 0]])
assert_array_equal(waveforms.unit_impulse(9, 'mid'),
[0, 0, 0, 0, 1, 0, 0, 0, 0])
def test_dtype(self):
imp = waveforms.unit_impulse(7)
assert_(np.issubdtype(imp.dtype, np.floating))
imp = waveforms.unit_impulse(5, 3, dtype=int)
assert_(np.issubdtype(imp.dtype, np.integer))
imp = waveforms.unit_impulse((5, 2), (3, 1), dtype=complex)
assert_(np.issubdtype(imp.dtype, np.complexfloating))