spkit.ramanujan_filter

spkit.ramanujan_filter(x, Pmax=10, Rcq=10, Rav=2, Th=0.2, Penalty=None, return_filters=False, apply_averaging=True)

Ramanujan Filter Banks for Estimation and Tracking of Periodicity

Ramanujan Filter Banks for Estimation and Tracking of Periodicity

Parameters:
x1d array, sequence of signal
Pmaxthe largest expected period.
RcqNumber of repeats in each Ramanujan filter
RavNumber of repeats in each averaging filter
ThOutputs of the RFB are thresholded to zero for all values less than Th*max(output)
Penalt = penalty for each period shape=(len(Pmax)),

If None, then set to 1, means no penalty

Returns:
y: 2d array of shape = (len(x),Pmax)

  • time vs period matrix, normalized

if return_filters==True,

  • also returns

  • FR : list of Ramanujan Filters

  • FA : list of Averaging Filters

See also

ramanujan_filter_prange, regularised_period_estimation, create_dictionary

Notes

References

  • [1] S.V. Tenneti and P. P. Vaidyanathan, “Ramanujan Filter Banks for Estimation and Tracking of Periodicity”, Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Brisbane, April 2015.

  • [2] P.P. Vaidyanathan and S.V. Tenneti, “Properties of Ramanujan Filter Banks”, Proc. European Signal Processing Conference, France, August 2015.

  • Python impletation is done by using matlab code version from - http://systems.caltech.edu/dsp/students/srikanth/Ramanujan/

Examples

#sp.ramanujan_filter
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
np.random.seed(2)
#period = 10 #SNR = 0
period = 8
x1 = np.zeros(30)
x2 = np.random.randn(period)
x2 = np.tile(x2,10)
x3 = np.zeros(30)
x  = np.r_[x1,x2,x3]
x_noise = sp.add_noise(x,snr_db=0)
Pmax=40
y,FR, FA = sp.ramanujan_filter(x_noise,Pmax=Pmax, Rcq=15, Rav=2, Th=0.2,return_filters=True)
print('top 10 periods: ',np.argsort(np.sum(y,0))[::-1][:10]+1)
plt.figure(figsize=(12,6))
plt.subplot(211)
plt.plot(x,label='signal: x')
plt.plot(x_noise, label='signal+noise: x_noise')
plt.text(5,3.5,f'signal with repitative patterns')
plt.xlim([0,len(x)])
#plt.xlabel('sample (n)')
plt.legend(bbox_to_anchor=(1,1))
plt.subplot(223)
im = plt.imshow(y.T,aspect='auto',cmap='jet',extent=[1,len(x_noise),Pmax,1])
plt.colorbar(im)
plt.xlabel('sample (n)')
plt.ylabel('period (in samples)')
plt.subplot(224)
plt.stem(np.arange(1,y.shape[1]+1),np.sum(y,0))
plt.xlabel('period (in samples)')
plt.ylabel('strength')
plt.tight_layout()
plt.show()
../../_images/spkit-ramanujan_filter-1.png

Examples using spkit.ramanujan_filter

Ramanujan Dictionary - with sparse penalty

Ramanujan Dictionary - with sparse penalty

Ramanujan Filter Banks Example

Ramanujan Filter Banks Example