Fast implementation of a general L/M rate changer by a filter bank structure

In this paper, we show that an L/M rate changer can be realized as a discrete time SISO (L,M) shift invariant system in form of a two-dimensional kernel function or a filter bank structure. Based on this realization, we can implement an L/M rate changer by a bank of filters with the average number of the coefficients in the filters in each channel is 1/L of the original L/M rate changer. Hence, the system is speed up by L. This helps the designer to design a sharp cutoff discrete time FIR filters in an L/M rate changer for some real time applications in video systems

Matrix Methods for the Dynamic Range Optimization of Continuous-TimeGm-CFilters

This paper presents a synthesis procedure for the optimization of the dynamic range of continuous-time fully differential G m - C filters. Such procedure builds up on a general extended state-space system representation which provides simple matrix algebra mechanisms to evaluate the noise and distortion performances of filters, as well as, the effect of amplitude and impedance scaling operations. Using these methods, an analytical technique for the dynamic range optimization of weakly nonlinear G m - C filters under power dissipation constraints is presented. The procedure is first explained for general filter structures and then illustrated with a simple biquadratic section

Classical sampling theorems in the context of multirate and polyphase digital filter bank structures

The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n ) with a Fourier transform vanishes for |ω|&ges;Lπ/M, where L and M are integers with L<M, can in principle be represented by reducing the data rate by the amount M/L. The digital polyphase framework is used as a convenient tool for the derivation as well as mechanization of the sampling theorem

Soft lithography replica molding of critically coupled polymer microring resonators

We use soft lithography replica molding to fabricate unclad polystyrene (PS) and clad SU-8 microring resonator filters. The PS resonator has an intrinsic quality factor of 1.0/spl times/10/sup 4/ at /spl lambda/=1.55 /spl mu/m, while that of the SU-8 resonator is 7100. The extinction ratios of the PS and SU-8 microring filters are -12 and -20 dB, respectively, with net insertion losses of 6.7 and 9.9 dB. The good quality factors and high extinction ratios of the microring resonator filters show the practicality of soft-lithography replica molding for the fabrication of integrated optical devices

Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system