# only solution in this case is to avoid aliasing in the first place :)
import numpy as np
from pwtools import mpl
from scipy.signal import hanning
from scipy.fftpack import fft
from pwtools.signal import fftsample, FIRFilter, pad_zeros
pi = np.pi
plt = mpl.plt
plots = mpl.prepare_plots(["freq", "filt_pad", "filt_nopad"])
nyq = 100 # Hz
df = 1.0 # Hz
dt, nstep = fftsample(nyq, df, mode="f")
t = np.linspace(0, 1, int(nstep))
filt1 = FIRFilter(cutoff=[10, 50], nyq=nyq, mode="bandpass", ripple=60, width=10)
filt2 = FIRFilter(cutoff=[10, 50], nyq=nyq, mode="bandpass", ntaps=100, window="hamming")
plots["freq"].ax.plot(filt1.w, abs(filt1.h), label="filt1")
plots["freq"].ax.plot(filt2.w, abs(filt2.h), label="filt2")
plots["freq"].ax.legend()
for pad in [True, False]:
x = np.sin(2 * pi * 20 * t) + np.sin(2 * pi * 80 * t)
if pad:
x = pad_zeros(x, nadd=len(x))
pl = plots["filt_pad"]
else:
pl = plots["filt_nopad"]
f = np.fft.fftfreq(len(x), dt)
print("not found, will skip fourier.x")
# For the calculation of nstep and dt, we increase `fmax` to
# fmax*fmax_extend_fac to lower dt. That way, the signal still contains
# frequencies up to `fmax`, but the FFT frequency axis does not end at exactly
# `fmax` but extends to higher values (we increase the Nyquist frequency).
df = 0.001
fmax = 1
fmax_extend_fac = 1.5
# number of frequencies contained in the signal
nfreq = 10
# time axis that assures that the fft catches all freqs up to and beyond fmax
# to avoid FFT aliasing
dt, nstep = signal.fftsample(fmax * fmax_extend_fac, df)
nstep = int(nstep)
taxis = np.linspace(0, dt * nstep, nstep, endpoint=False)
##print "dt [s]:", dt
##print "dt [Hartree]:", dt/constants.th
##print "nstep:", nstep
##print "fmax [Hz]:", fmax
##print "nfreq:", nfreq
###############################################################################
# 1d arrays
###############################################################################
# First, we treat a simple 1d signal to test the math.
# and just using a bandpass around you desired frequency band won't help. The
# only solution in this case is to avoid aliasing in the first place :)
import numpy as np
from pwtools import mpl
from scipy.signal import hanning
from scipy.fftpack import fft
from pwtools.signal import fftsample, FIRFilter, pad_zeros
pi = np.pi
plt = mpl.plt
plots = mpl.prepare_plots(['freq', 'filt_pad', 'filt_nopad'])
nyq = 100 # Hz
df = 1.0 # Hz
dt, nstep = fftsample(nyq, df, mode='f')
t = np.linspace(0, 1, int(nstep))
filt1 = FIRFilter(cutoff=[10, 50],
nyq=nyq,
mode='bandpass',
ripple=60,
width=10)
filt2 = FIRFilter(cutoff=[10, 50],
nyq=nyq,
mode='bandpass',
ntaps=100,
window='hamming')
plots['freq'].ax.plot(filt1.w, abs(filt1.h), label='filt1')
plots['freq'].ax.plot(filt2.w, abs(filt2.h), label='filt2')
plots['freq'].ax.legend()
print "not found, will skip fourier.x" # For the calculation of nstep and dt, we increase `fmax` to # fmax*fmax_extend_fac to lower dt. That way, the signal still contains # frequencies up to `fmax`, but the FFT frequency axis does not end at exactly # `fmax` but extends to higher values (we increase the Nyquist frequency). df = 0.001 fmax = 1 fmax_extend_fac = 1.5 # number of frequencies contained in the signal nfreq = 10 # time axis that assures that the fft catches all freqs up to and beyond fmax # to avoid FFT aliasing dt, nstep = signal.fftsample(fmax*fmax_extend_fac, df) nstep = int(nstep) taxis = np.linspace(0, dt*nstep, nstep, endpoint=False) ##print "dt [s]:", dt ##print "dt [Hartree]:", dt/constants.th ##print "nstep:", nstep ##print "fmax [Hz]:", fmax ##print "nfreq:", nfreq ############################################################################### # 1d arrays ############################################################################### # First, we treat a simple 1d signal to test the math.
