Filter design for MIMO sampling and reconstruction

We address the problem of finite impulse response (FIR) filter design for uniform multiple-input multiple-output (MIMO) sampling. This scheme encompasses Papoulis' generalized sampling and several nonuniform sampling schemes as special cases. The input signals are modeled as either continuous-time or discrete-time multiband input signals, with different band structures. We present conditions on the channel and the sampling rate that allow perfect inversion of the channel. Additionally, we provide a stronger set of conditions under which the reconstruction filters can be chosen to have frequency responses that are continuous. We also provide conditions for the existence of FIR perfect reconstruction filters, and when such do not exist, we address the optimal approximation of the ideal filters using FIR filters and a minmax l/sub 2/ end-to-end distortion criterion. The design problem is then reduced to a standard semi-infinite linear program. An example design of FIR reconstruction filters is given.

[1]  A. W. M. van den Enden,et al.  Discrete Time Signal Processing , 1989 .

[2]  J. L. Brown.  Sampling expansions for multiband signals , 1985, IEEE Trans. Acoust. Speech Signal Process..

[3]  Thomas W. Parks,et al.  Linear periodic systems and multirate filter design , 1994, IEEE Trans. Signal Process..

[4]  Meir Feder,et al.  Vector sampling expansion , 2000, IEEE Trans. Signal Process..

[5]  John M. Cioffi,et al.  Spatio-temporal coding for wireless communication , 1998, IEEE Trans. Commun..

[6]  Yoram Bresler,et al.  Multiple-input multiple-output sampling: necessary density conditions , 2004, IEEE Transactions on Information Theory.

[7]  Geoffrey Ye Li,et al.  Adaptive Blind Source Separation and Equalization for Multiple-Input/Multiple-Output Systems , 1998, IEEE Trans. Inf. Theory.

[8]  K. Cheung.  A Multidimensional Extension of Papoulis’ Generalized Sampling Expansion with the Application in Minimum Density Sampling , 1993 .

[9]  Xiang-Gen Xia,et al.  New precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal FIR equalizers , 1997, IEEE Trans. Signal Process..

[10]  Cormac Herley,et al.  Minimum rate sampling of signals with arbitrary frequency support , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[11]  Y. Bresler,et al.  Spectrum-blind minimum-rate sampling and reconstruction of 2-D multiband signals , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[12]  Zhishun Wang,et al.  Blind separation of slow waves and spikes from gastrointestinal myoelectrical recordings , 2001, IEEE Transactions on Information Technology in Biomedicine.

[13]  Mihai Anitescu,et al.  The role of linear semi-infinite programming in signal-adapted QMF bank design , 1997, IEEE Trans. Signal Process..

[14]  Yunxin Zhao,et al.  Adaptive co-channel speech separation and recognition , 1999, IEEE Trans. Speech Audio Process..

[15]  Jian Yang,et al.  On joint transmitter and receiver optimization for multiple-input-multiple-output (MIMO) transmission systems , 1994, IEEE Trans. Commun..

[16]  William J. Fitzgerald,et al.  Periodic nonuniform sampling of multiband signals , 1992, Signal Process..

[17]  R. Marks,et al.  Imaging sampling below the Nyquist density without aliasing , 1990 .

[18]  Alberto González,et al.  Fast transversal filters for deconvolution in multichannel sound reproduction , 2001, IEEE Trans. Speech Audio Process..

[19]  A. Papoulis,et al.  Generalized sampling expansion , 1977 .

[20]  Yoram Bresler,et al.  Sampling theorems for uniform and periodic nonuniform MIMO sampling of multiband signals , 2003, IEEE Trans. Signal Process..

[21]  W. Rudin.  Principles of mathematical analysis , 1964 .

[22]  Cormac Herley,et al.  Minimum rate sampling and reconstruction of signals with arbitrary frequency support , 1999, IEEE Trans. Inf. Theory.

[23]  Lee C. Potter,et al.  MIMO FIR equalizers and orders , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[24]  John M. Cioffi,et al.  Multichannel signal processing for multiple-head digital magnetic recording , 1994 .

[25]  G Harikumar,et al.  Exact image deconvolution from multiple FIR blurs , 1999, IEEE Trans. Image Process..

[26]  Yves Goussard,et al.  Multichannel seismic deconvolution , 1993, IEEE Trans. Geosci. Remote. Sens..

[27]  Carlos A. Berenstein,et al.  On explicit solutions to the Bezout equation , 1984 .

[28]  Raman C. Venkataramani,et al.  Sub-Nyquist Multicoset and MIMO Sampling: Perfect Reconstruction, Performance Analysis, and Necessary Density Conditions , 2001 .

[29]  Bede Liu,et al.  Sampling representations and the optimum reconstruction of signals , 1965, IEEE Trans. Inf. Theory.

[30]  P. P. Vaidyanathan,et al.  MIMO biorthogonal partners and applications , 2002, IEEE Trans. Signal Process..

[31]  Asoke K. Nandi,et al.  Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation , 2001, IEEE Transactions on Biomedical Engineering.

[32]  Ramachandra G. Shenoy,et al.  Nonuniform sampling of signals and applications , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[33]  H. Landau.  Necessary density conditions for sampling and interpolation of certain entire functions , 1967 .

[34]  J. R. Higgins.  Sampling theory in Fourier and signal analysis : foundations , 1996 .

[35]  Yoram Bresler,et al.  Perfect reconstruction formulas and bounds on aliasing error in sub-nyquist nonuniform sampling of multiband signals , 2000, IEEE Trans. Inf. Theory.

[36]  Gautam Appa,et al.  Linear Programming in Infinite-Dimensional Spaces , 1989 .

[37]  David D. Falconer,et al.  Suppression of adjacent-channel, cochannel, and intersymbol interference by equalizers and linear combiners , 1994, IEEE Trans. Commun..

[38]  Yoram Bresler,et al.  Perfect blind restoration of images blurred by multiple filters: theory and efficient algorithms , 1999, IEEE Trans. Image Process..

[39]  P. P. Vaidyanathan,et al.  Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks , 1990, IEEE Trans. Acoust. Speech Signal Process..

[40]  Ping Feng,et al.  Spectrum-blind minimum-rate sampling and reconstruction of multiband signals , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[41]  Yoram Bresler,et al.  Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals , 2001, IEEE Trans. Signal Process..