def filter_trig_poly(u, h, dt, M):
"""
Filter a trigonometric polynomial with a filter's impulse response.
Parameters
----------
u : numpy.ndarray
Input signal.
h : numpy.ndarray
Impulse response of filter.
dt : float
Time resolution.
M : int
Trigonometric polynomial order.
Returns
-------
v : numpy.ndarray
Filtered signal.
Notes
-----
Assumes that `u` is defined over times `dt*arange(0, len(t))` and
that `dt*len(u)` is equal to the period of the trigonometric polynomial.
"""
# Get the Dirichlet coefficients of the signal:
am = tp.get_dirichlet_coeffs(u, dt, M)
# Get the Dirichlet coefficients of the filter:
hm = tp.get_dirichlet_coeffs(h, dt, M)
# Construct the filtered signal using the above coefficients:
T = dt*len(u)
Omega = 2*np.pi*M/T
t = np.arange(0, len(u))*dt
v = np.zeros(len(u), np.complex)
for m in xrange(-M, M+1):
v += hm[m+M]*am[m+M]*em(m, t, Omega, M)*np.sqrt(T)/dt
return np.real(v)
def filter_trig_poly(u, h, dt, M):
"""
Filter a trigonometric polynomial with a filter's impulse response.
Parameters
----------
u : numpy.ndarray
Input signal.
h : numpy.ndarray
Impulse response of filter.
dt : float
Time resolution.
M : int
Trigonometric polynomial order.
Returns
-------
v : numpy.ndarray
Filtered signal.
Notes
-----
Assumes that `u` is defined over times `dt*arange(0, len(t))` and
that `dt*len(u)` is equal to the period of the trigonometric polynomial.
"""
# Get the Dirichlet coefficients of the signal:
am = tp.get_dirichlet_coeffs(u, dt, M)
# Get the Dirichlet coefficients of the filter:
hm = tp.get_dirichlet_coeffs(h, dt, M)
# Construct the filtered signal using the above coefficients:
T = dt * len(u)
Omega = 2 * np.pi * M / T
t = np.arange(0, len(u)) * dt
v = np.zeros(len(u), np.complex)
for m in xrange(-M, M + 1):
v += hm[m + M] * am[m + M] * em(m, t, Omega, M) * np.sqrt(T) / dt
return np.real(v)
N = len(u)
return np.real(np.fft.ifft(np.fft.fft(np.hstack((u, np.zeros(len(h)-1))))*\
np.fft.fft(np.hstack((h, np.zeros(len(u)-1))))))[0:N]
if __name__ == '__main__':
print 'generating trigonometric polynomial signal..'
M = 250
Omega = 2*np.pi*2000
T = 2*np.pi*M/Omega
dt = 1e-5
t = np.arange(0, T, dt)
u = tp.gen_trig_poly(T, dt, M)
am_rec = tp.get_dirichlet_coeffs(u, dt, M)
# Try to recover the Dirichlet coefficients of the generated signal
# using different methods. Note that this only works if u contains an
# entire period of the signal (i.e., arange(0, T, dt)):
print 'reconstructing signal from recovered coefficients..'
u_rec = tp.gen_trig_poly(T, dt, am_rec)
pl.plot_compare(t, u, u_rec, 'Signal Reconstruction',
output_name + str(output_count) + output_ext)
output_count += 1
# Create a filter:
h = make_gammatone(t, 16, 0)
hm = tp.get_dirichlet_coeffs(h, dt, M)
h_rec = tp.gen_trig_poly(T, dt, hm)
pl.plot_compare(t, h, h_rec, 'Filter Reconstruction',
return np.real(np.fft.ifft(np.fft.fft(np.hstack((u, np.zeros(len(h)-1))))*\
np.fft.fft(np.hstack((h, np.zeros(len(u)-1))))))[0:N]
if __name__ == '__main__':
print 'generating trigonometric polynomial signal..'
M = 250
Omega = 2 * np.pi * 2000
T = 2 * np.pi * M / Omega
dt = 1e-5
t = np.arange(0, T, dt)
u = tp.gen_trig_poly(T, dt, M)
am_rec = tp.get_dirichlet_coeffs(u, dt, M)
# Try to recover the Dirichlet coefficients of the generated signal
# using different methods. Note that this only works if u contains an
# entire period of the signal (i.e., arange(0, T, dt)):
print 'reconstructing signal from recovered coefficients..'
u_rec = tp.gen_trig_poly(T, dt, am_rec)
pl.plot_compare(t, u, u_rec, 'Signal Reconstruction',
output_name + str(output_count) + output_ext)
output_count += 1
# Create a filter:
h = make_gammatone(t, 16, 0)
hm = tp.get_dirichlet_coeffs(h, dt, M)
h_rec = tp.gen_trig_poly(T, dt, hm)
pl.plot_compare(t, h, h_rec, 'Filter Reconstruction',