class BandPassExample(object):
def __init__(self):
self.su = SignalUtil()
def getSignal(self, a, t, f0):
x = 0.1 * np.sin(2 * np.pi * 1.2 * np.sqrt(t))
x += 0.01 * np.cos(2 * np.pi * 312 * t + 0.1)
x += a * np.cos(2 * np.pi * f0 * t + .11)
x += 0.03 * np.cos(2 * np.pi * 2000 * t)
return x
def getEEGSignal(self):
scriptPath = os.path.dirname(os.path.abspath(__file__))
return EEGTableFileUtil().readFile(scriptPath + "/../../examples/example_1024.csv")
def plotBBF(self, fs, lowcut, highcut):
# Plot the frequency response for a few different orders.
plt.figure(1)
plt.clf()
for order in [2, 4, 8]:
b, a = self.su.butterBandpass(lowcut, highcut, fs, order=order)
w, h = freqz(b, a, worN=2000)
plt.doPlot((fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)
plt.doPlot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)], '--', label='sqrt(0.5)')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(True)
plt.legend(loc='best')
def getDuration(self, data):
time = data.getColumn("Timestamp")
duration = time[len(time) - 1] - time[0]
return duration
def plotEEGSignal(self):
# Filter a noisy signal.
data = self.getEEGSignal()
fs = data.getSamplingRate();
x = data.getColumn("F3")
x = SignalUtil().normalize(x)
duration = self.getDuration(data)
t = np.linspace(0, duration, len(x), endpoint=False)
plt.figure(2)
plt.clf()
plt.doPlot(t, x, label='normalized signal')
for label, (lowcut, highcut) in EEGUtil().channel_ranges.iteritems():
if label == "alpha":
y = self.su.butterBandpassFilter(x, lowcut, highcut, fs, order=6)
plt.doPlot(t, y, label='%s (%d - %dHz)' % (label, lowcut, highcut))
plt.xlabel('time (seconds)')
plt.grid(True)
plt.axis('tight')
plt.legend(loc='upper left')
def plotSoundSignal(self):
# Filter a noisy signal.
path = "../../examples/"
fs, s1 = wavfile.read(path + '12000hz.wav')
if len(s1.shape) == 2:
s1 = s1[:,0]
n = float(len(s1))
t = arange(0, n, 1)
t = t / fs
t = t * 1000 #scale to milliseconds
plt.figure(2)
plt.clf()
plt.doPlot(t, s1, label='sound signal')
y = self.su.butterBandpassFilter(s1, 11000, 13000, fs, order=6)
#wavfile.write(path + '12000hz_cut.wav', fs, y)
plt.doPlot(t, y, label='%s (%d - %dHz)' % ("12000Hz", 11000, 13000))
plt.xlabel('time (seconds)')
plt.grid(True)
plt.axis('tight')
plt.legend(loc='upper left')
def plotSignal(self, fs, lowcut, highcut):
# Filter a noisy signal.
T = 0.05
nsamples = T * fs
t = np.linspace(0, T, nsamples, endpoint=False)
a = 0.02
f0 = 600.0 # frequency
x = self.getSignal(a, t, f0)
plt.figure(2)
plt.clf()
plt.doPlot(t, x, label='Noisy signal')
y = self.butterBandpassFilter(x, lowcut, highcut, fs, order=6)
plt.doPlot(t, y, label='Filtered signal (%g Hz)' % f0)
plt.xlabel('time (seconds)')
plt.hlines([-a, a], 0, T, linestyles='--')
plt.grid(True)
plt.axis('tight')
plt.legend(loc='upper left')
def main(self):
# Sample rate and desired cutoff frequencies (in Hz).
fs = 5000.0
lowcut = 500.0
highcut = 1250.0
self.plotBBF(fs, lowcut, highcut)
#self.plotSignal(fs, lowcut, highcut)
self.plotEEGSignal()
#self.plotSoundSignal()
plt.show()
class TestFrequencyFilter(unittest.TestCase):
def setUp(self):
self.util = SignalUtil()
self._setSignalParams()
def _setSignalParams(self, offset=0, length=-1):
self.samplingRate, self.data= self._readSoundFile(offset=offset, length=length)
self.n = len(self.data)
self.nUniquePts = ceil((self.n+1)/2.0)
self.freqArray = np.arange(0, self.nUniquePts, 1.0) * (self.samplingRate / self.n)
def test_butterBandpass(self):
samplingRate = 32
i = samplingRate / 4
b, a = self.util.butterBandpass(i-1, i+1, samplingRate)
_, h = freqz(b, a, worN=samplingRate*4)
h = abs(h)
self.assertEqual(np.argmax(h), len(h)/2)
self.assertAlmostEqual(max(h), 1, delta=0.1)
self.assertAlmostEqual(h[0], 0, delta=0.01)
self.assertAlmostEqual(h[len(h)-1], 0, delta=0.01)
def test_butterBandpass_egde(self):
# no signal allowed
b, a = self.util.butterBandpass(5, 5, 16)
_, h = freqz(b, a, worN=32)
self.assertEquals(np.count_nonzero(abs(h)), 0)
# everything gets through (except 0)
b, a = self.util.butterBandpass(0, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(0.5, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(-1, 9, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
def test_butterBandpassFilter(self):
x = [1, -1, 1, -1]
_ = self.util.butterBandpassFilter(x, 1, 2, 10)
def _readSoundFile(self, fileName='12000hz.wav', offset=0, length=-1):
samplingRate, data = wavfile.read(PATH + fileName)
if len(data.shape) == 2:
data = data[:,0]
if(length > -1):
data = data[offset:offset+length]
data = self.util.normalize(data)
return samplingRate, data
def _getMaxFrequency(self, data, freqArray):
fft = FFTUtil().fft(data)
return freqArray[np.argmax(fft)]
def test_butterBandpassFilter_original(self):
freqMax = self._getMaxFrequency(self.data, self.freqArray)
self.assertAlmostEqual(freqMax, 12000.0, delta= 1000)
def test_butterBandpassFilter_filterNoCut(self):
cut = self.util.butterBandpassFilter(self.data, 1000, self.samplingRate/2-1000, self.samplingRate)
freqMax = self._getMaxFrequency(cut, self.freqArray)
self.assertAlmostEqual(freqMax, 12000.0, delta= 1000)
def test_butterBandpassFilter_filterAroundMax(self):
cut = self.util.butterBandpassFilter(self.data, 11000, 13000, self.samplingRate)
freqMax = self._getMaxFrequency(cut, self.freqArray)
self.assertAlmostEqual(freqMax, 12000.0, delta= 1000)
def test_butterBandpassFilter_filterAboveMax(self):
cut = self.util.butterBandpassFilter(self.data, 0, 2000, self.samplingRate)
freqMax = self._getMaxFrequency(cut, self.freqArray)
self.assertNotEqual(freqMax, 12000.0)
self.assertAlmostEqual(freqMax, 1000.0, delta= 1000)
def test_butterBandpassFilter_filterBeyondMax(self):
cut = self.util.butterBandpassFilter(self.data, self.samplingRate/2-2000, self.samplingRate/2, self.samplingRate)
freqMax = self._getMaxFrequency(cut, self.freqArray)
self.assertNotEqual(freqMax, 12000.0)
self.assertAlmostEqual(freqMax, self.samplingRate/2-1000, delta= 1000)
def test_butterBandpassFilter_short(self):
self._setSignalParams(length=4)
freqMax = self._getMaxFrequency(self.data, self.freqArray)
self.assertAlmostEqual(freqMax, 12000.0, delta= 1000)
cut = self.util.butterBandpassFilter(self.data, 1000, self.samplingRate/2-1000, self.samplingRate)
freqMax = self._getMaxFrequency(cut, self.freqArray)
self.assertAlmostEqual(freqMax, 12000.0, delta= 1000)
def test_butterBandpassFilter_originalAndShort(self):
cutOrig = self.util.butterBandpassFilter(self.data, 1000, self.samplingRate/2-1000, self.samplingRate)
freqMaxOrig = self._getMaxFrequency(self.data, self.freqArray)
self._setSignalParams(length=4)
cutShort = self.util.butterBandpassFilter(self.data, 1000, self.samplingRate/2-1000, self.samplingRate)
freqMaxShort = self._getMaxFrequency(self.data, self.freqArray)
self.assertAlmostEqual(freqMaxShort, freqMaxOrig, delta=1000)
for i in range(len(cutShort)):
self.assertAlmostEqual(cutOrig[i], cutShort[i], delta=0.02)
