spkit.ramanujan_filter_prange

spkit.ramanujan_filter_prange(x, Pmin=1, Pmax=10, skip=1, Rcq=10, Rav=2, thr=0.2, Penalty=None, return_filters=False, apply_averaging=True)

Ramanujan Filter Banks for Estimation and Tracking of Periodicity with given range.

Ramanujan Filter Banks for Estimation and Tracking of Periodicity

  • for range of period given by Pmin and Pmax.

Parameters:
x = 1d array, sequence of signal
Pmin = the smallest expected period. (default=1)
Pmax = the largest expected period.
skip = int >=1: if to skip period (default=1 –> no skipping) (>1 is not recomended)
Rcq = Number of repeats in each Ramanujan filter
Rav = Number of repeats in each averaging filter
thr = Outputs of the RFB are thresholded to zero for all values less than Th*max(output)
Penalty = penalty for each period shape=(len(Pmax)),

If None, then set to 1, means no penalty

apply_averaging: bool, if False, no averaging is applied (deault=True)
return_filters: bool, ifTrue, return FR - Ramanujan and FA - Averaging filters
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, 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_prange
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)
Pmin = 4
Pmax = 20
y,plist, FR, FA = sp.ramanujan_filter_prange(x_noise,Pmin=Pmin, Pmax=Pmax, skip=2, Rcq=10, Rav=2, thr=0.2,return_filters=True)
idx = np.argsort(np.sum(y,0))[::-1]
print('top 10 periods: ',plist[idx[:10]])
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,Pmin])
plt.yticks(plist)
plt.colorbar(im)
plt.xlabel('sample (n)')
plt.ylabel('period (in samples)')
plt.subplot(224)
plt.stem(plist,np.sum(y,0))
plt.xlabel('period (in samples)')
plt.ylabel('strength')
plt.tight_layout()
plt.show()
../../_images/spkit-ramanujan_filter_prange-1.png

Examples using spkit.ramanujan_filter_prange

Ramanujan Filter Banks Example

Ramanujan Filter Banks Example