README.md

1D FIR Sparse Filter Design Using Optimization

This work implements the 1D FIR sparse filter design technique proposed in the following paper for lowpass, highpass, bandpass and bandstop filters.

[1] W.-S. Lu and T. Hinamoto, "Digital flters with sparse coefficients," in Proceedings of 2010 IEEE International Symposium on Circuits and Systems. IEEE, 2010, pp. 169-172.

Functions

• L2_sparse(N1, f_type, fp_para, fa_para, mu, delta)

Designs the desired standard filters in the least squares sense. Outputs the impulse response, number of zeros, and the L-2 error.

• L_inf_sparse(N1, f_type, fp_para, fa_para, mu, delta)

Designes the desired standard filters in the minimax sense. Outputs the impulse response, number of zeros, and the L_inf error

• QMat(N1, f_type, fp_para, fa_para)

Supporting function for L2_sparse. Calculates the Hessian matrix.

• pCol(N1, f_type, fp_para)

Supporting function for L2_sparse. Calculates the gradient vector needed for the first phase of L2 sparse filter design.

• freqGrids(N1, f_type, fp_para, fa_para)

Supporting function for L_inf_sparse. Outputs a frequency grid of passband and stopband frequencies.

Function parameters

• N1: filter order (even integer).
• f_type: 1 for lowpass, 2 for highpass, 3 for bandpass, and 4 for bandstop.
• fp_para: Normalized passband frequency fp for types 1 and 2, [fp1 fp2] for types 3 and 4.
• fa_para: Normalized stopband frequency fa for types 1 and 2, [fa1 fa2] for types 3 and 4.
• mu: regularization parameter.
• delta: threshold for hardthresholding.

Dependencies

• CVX