Title :
A constrained weighted least squares approach for time-frequency distribution kernel design
Author :
Amin, Moeness G. ; Venkatesan, Gopal T. ; Carroll, James F.
Author_Institution :
Dept. of Electr. Eng., Villanova Univ., PA, USA
fDate :
5/1/1996 12:00:00 AM
Abstract :
In most applications of time-frequency (t-f) distributions, the t-f kernel is of finite extent and applied to discrete time signals. This paper introduces a matrix-based approach for t-f distribution kernel design. In this new approach, the optimum kernel is obtained as the solution of a linearly constrained weighted least squares minimization problem in which the kernel is vectorial and the constraints form a linear subspace. Similar to FIR temporal and spatial constrained least squares (LS) design methods, the passband, stopband, and transition band of an ideal kernel are first specified. The optimum kernel that best approximates the ideal kernel in the LS error sense, and simultaneously satisfies the multiple linear constraints, is then obtained using closed-form expressions. This proposed design method embodies a well-structured procedure for obtaining fixed and data-dependent kernels that are difficult to obtain using other design approaches
Keywords :
discrete time systems; least mean squares methods; matrix algebra; minimisation; signal processing; statistical analysis; time-frequency analysis; closed-form expressions; constrained weighted least squares approach; data-dependent kernels; design method; discrete time signal; fixed kernels; linear subspace; linearly constrained weighted least squares minimization problem; matrix-based approach; optimum kernel; passband; stopband; t-f kernel; time-frequency distribution kernel design; transition band; Closed-form solution; Design methodology; Finite impulse response filter; Kernel; Least squares approximation; Least squares methods; Passband; Signal design; Subspace constraints; Time frequency analysis;
Journal_Title :
Signal Processing, IEEE Transactions on