Design of Hybrid Filter Banks for AnalogDigital Conversion_ieee.pdf

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Design of Hybrid Filter Banks for AnalogDigital Conversion_ieee

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Abstract—This paper presents design algorithms for hybrid
filter banks (HFB’s) for high-speed, high-resolution conversion
between analog and digital signals. The HFB is an unconventional
class of filter bank that employs both analog and digital
filters. When used in conjunction with an array of slower speed
converters, the HFB improves the speed and resolution of the
conversion compared with the standard time-interleaved array
conversion technique. The analog and digital filters in the HFB
must be designed so that they adequately isolate the channels and
do not introduce reconstruction errors that limit the resolution of
the system. To design continuous-time analog filters for HFB’s,
a discrete-time-to-continuous-time (“Z-to-S”) transform is developed
to convert a perfect reconstruction (PR) discrete-time filter
bank into a near-PR HFB; a computationally efficient algorithm
based on the fast Fourier transform (FFT) is developed to design
the digital filters for HFB’s. A two-channel HFB is designed
with sixth-order continuous-time analog filters and length 64
FIR digital filters that yield ... ....

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VI. CONCLUSIONS
This paper develops efficient algorithms for the design
of -channel, maximally decimated, uniform bandwidth
continuous-time HFB’s and discrete-time HFB’s. The
continuous-time hybrid filter bank analog-to-digital converter
employs continuous-time analog analysis filters and discretetime
digital synthesis filters. The filters are designed with
enough stopband attenuation to attenuate the effects of
mismatches between the converters in the array, which
otherwise severely limit the resolution of the system. The
filter cutoff should be as sharp as possible to simplify the
calibration. This paper develops a discrete-time-to-continuoustime
(“ -to- ”) mathematical transform similar to the Pade’
approximation, which converts a discrete-time filter to a
continuous-time filter with approximately the same frequency
response. This enables PR discrete-time filter banks to be
transformed into near-PR continuous-time hybrid filter banks.
A stable second-order transform has frequency-response
matching better than 28 dB, and a stable fourth-order
transform has matching better than 99 dB. Note that a
th-order transform converts an th-order discrete-time filter
into a continuous-time filter with order ... ...

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REFERENCES
[1] R. E. Crochiere and L. R. Rabiner, Multirate Signal Processing. Englewood
Cliffs, NJ: Prentice-Hall, 1983.
[2] R. V. Cox, D. E. Boch, K. B. Bauer, J. D. Johnston, and J. H. Snyder,
“The analog voice privacy system,” Proc. IEEE Int. Conf. Acoust.,
Speech, Signal Process., Apr. 1986, pp. 341–344.
[3] J. Kovacevic, D. J. Le Gall, and M. Vetterli, “Image coding with
windowed modulated filter banks,” Proc. IEEE Conf. Acoust., Speech,
Signal Process., May 1989, pp. 1949–1952.

[5] M. Vetterli, “A theory of multirate filter banks,” IEEE Trans. Acoust.,
Speech, Signal Processing, vol. ASSP-35, pp. 356–372, Mar. 1987.
[6] M. J. Smith and T. P. Barnwell, III, “Exact reconstruction techniques
for tree-structured subband coders,” IEEE Trans. Acoust., Speech, Signal
Processing, vol. ASSP-34, pp. 434–441, June 1986.
[7] G. Strang and T. Q. Nguyen, Wavelets and Filter Banks. Cambridge,
MA: Wellesley-Cambridge Press, 1996.
[8] S. R. Velazquez, “Hybrid filter banks for analog/digital conversion,”
Ph.D. dissertation, Mass. Inst. Technol., Cambridge, June 1997.

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