frequency representation for signal separation.
In this paper we discuss an approach for separating the robustness and location of cross terms on the auto terms.
that ak , K and maximum degree of the polynomial phase is the mean of the component frequencies at that instant.
include the Born Jordan kernel and cone kernel representation and therefore will intersect at a point in the parameter space.
CKR  constrains the temporal smoothing so that the spectral the maximum value attained in the (m, c) space.
signal higher order distributions like polynomial Wigner-Ville 0(v) 0(v) 0. we show the hough transform parameters in the TF domain. Further. Therefore it is expected to perform better for sinusoids for the following reason. ∗ denotes those components that were not detected by Hough introduce difficulty for higher order polynomial phase signal. 1.5156(m). But for polynomial Wigner-Ville representation cross terms will Note: The true value of IF are 3Hz. *(v) frequency representation.48(m). *(v) *(m). transform. . O UR A PPROACH M EAN ( M ) AND VARIANCE ( V ) IN THE IF ESTIMATES OF FOUR Our signal separation approach is based on choosing an COMPONENT SIGNAL USING H OUGH T RANSFORM AND CKR optimal time frequency representation for the given signal SNR(dB) First Second Third Fourth and applying hough transform on the chosen optimal time 0 3. The Wigner-Ville representation is 0. 7. 13. Therefore L- Wigner representation computed with a knowledge of signal separation in the time frequency domain will lead to an optimal to 10 dB. Moreover the dimension of the parameter the TF domain. The hough transform performance deteriorates around 6dB SNR. For multi-component signals the 0. *(v) component linear signals. 7Hz.12(m).093(v) 1.014(v) known to be optimal time frequency representation for single 3 3. S IMULATION AND D ISCUSSION theoretical performance bounds for parameters estimated using We consider four component signal composed of sinusoids TFR and hough transform..014(v) reduced interference distribution using Born-Jordan kernel is 6 3. The CKR is computed and the hough the performance of polynomial Wigner-Ville representation transform of CKR is obtained. If the signal tracks are represented by a delta function the number points in a particular bin (representing the parameter of the signal) increases when compared to the other bins in the parameter space. tracks in the hough transform domain. C ONCLUSION AND F UTURE W ORK Fig. The detected peaks are used to represent the regions in the CKR domain and an IF estimate is made based on the local peaks. The top row right and top left windows show the CKR of four component In this paper we shown that the performance of separa- signal at 5 dB and 15 dB SNR. 13Hz and 20Hz at 0. These peaks give an initial estimate of the IF law of each component.42(m).15(m). Therefore SNR seen in the hough transform domain is high for optimal TFRs. We detect the distinct signal components by identifying peaks in the Hough transform domain.42(m). TABLE I III. *(v) *(m). both the mean and variance. below which it fails to detect the cubic chirps.43(m).5(v) optimal. 20. As a part of further work we are obtaining IV.42(m). 7.19(v) distribution  or the L-Wigner distribution  is optimal. The resulting error in estimate i.014(v) 0.014(v) 0. CKR and associated hough transform of a four component signal. is given for all the four signal components in Table I.3828(m). The hough transform of the CKR is computed TFR for polynomial phase signals (here we ensure that there by integrating in the TF domain along all possible paths in are no cross terms). The bottom right and left windows show the tion multi-component using time frequency representation and associated hough transform.015s. In this paper.07(v) 0. *(m). 20. The sinusoids in the TFR domain is detected up to 3dB. The realization of polynomial Wigner-Ville representation for multi component signals is discussed in . 7. In general for single component polynomial phase 7 3.164(m).e. 0(v) 0(v) 0. We are also working on comparing and cubic chirps.5156(m). The hough performance of our approach using simulation results and the transform of the four component signals is shown in figure importance of choosing optimal time frequency representation 1. highlighted the importance of using optimal TFR for the given signal. 13. V.4765(m). Further we have also given insights on the perfor- mance analysis. Here we use peaks in the hough transform space to which Hough transform maps the time frequency domain as the initial estimates of the signal track and then representation is also decided based on the greatest degree look for peaks around the local region represented by these of the polynomial phase signal. 7. *(m). Here it is important to note that the CKR is an optimal TFR for sinusoids alone. The CKR and hough transform and L-Wigner representation for signal separation of multi of CKR is obtained for various SNRs ranging from 0dB component signals. There are four peaks corresponding to the four signal for signal separation.
 J. 1999. Jan 1996. 216-220. IEEE Transactions on Signal Processing.Stankovic. pp. ”A Survey of Hough Transform”. 1988. pp.J. IEEE Transactions on Signal Processing. NJ.E. 42. L.J. 22-25. Vol. ”Polynomial Wigner-Ville distribution and their relationship to time varying higher order spectra”. Computer Vision Graphics and Image Processing. ” Time Frequency Analysis”. 1990. No. 5. .Marks. IEEE Signal Processing Letters.  L.J. 38. ”The use of cone shaped kernels for generalized time-frequency representations for non-stationary signals”. 1084- 1091. 1994.  L. 3. Chapter 5.  L. 47(1). 87-116. ”Cone-kernel representation versus in- stantaneous power spectrum”.  Y.Stankovic. Speech. pp.Cohen. 250-254. Signal Processing. R EFERENCES  B.Viswanath and T. IEEE Transaction on Acoustic.Zhao.Sreenivas.V. Eaglewood Cliffs.Kittler.Boashash and O’shea.Illinworth and J. pp. pp. 44. 7.Atlas and R. ”L-Class of time-frequency distributions”. Prentice Hall. ”On the Realization of the Polynomial WignerVille Dis- tribution for Multicomponent Signals”. 1995.  G. IEEE Signal Processing Letters. July 1998.
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