It is well known that if each coefficient value of a digital filter is a sum of signed power-of-two (SPT) terms, the filter can be implemented without using multipliers. In the past decade, several methods have been developed for the design of filters whose coefficient values are sums of SPT terms. Most of these methods are for the design of filters where all the coefficient values have the same number of SPT terms. It has also been demonstrated recently that significant advantage can be achieved if the coefficient values are allocated with different number of SPT terms while keeping the total number of SPT terms for the filter fixed. In this paper, we present a new method for allocating the number of SPT terms to each coefficient value. In our method, the number of SPT terms allocated to a coefficient is determined by the statistical quantization step-size of that coefficient and the sensitivity of the frequency response of the filter to that coefficient. After the assignment of the SPT terms, an integer-programming algorithm is used to optimize the coefficient values. Our technique yields excellent results but does not guarantee optimum assignment of SPT terms. Nevertheless, for any particular assignment of SPT terms, the result obtained is optimum with respect to that assignment.

Signed Power-of-Two Term Allocation Scheme for the Design of Digital Filters

Signed power-of-two term allocation scheme for the design of digital filters

A 65-nm digitally modulated polar transmitter incorporates a fully integrated, efficient 2.4-GHz switching Inverse Class-D power amplifier. Low-power digital filtering on the amplitude path helps remove spectral images for coexistence. The transmitter integrates the complete LO distribution network and digital drivers. Operating from a 1-V supply, the PA has 21.8-dBm peak output power with 44% efficiency. Simple static predistortion helps the transmitter meet EVM and mask requirements of 802.11g 54-Mb/s WLAN data with 18% average efficiency.

An Efficient Mixed-Signal 2.4-GHz Polar Power Amplifier in 65-nm CMOS Technology

An efficient two-stage algorithm is presented for designing finite-impulse response (FIR) filters that employ sums of signed-powers-of-two (SPT) coefficients. In the first stage, a prototype filter is designed using a fast time-domain approximation. This is followed, in the second stage, where the design problem is formulated as a dynamic-programming-like recursive optimization problem, by a trellis search that optimizes the filter's frequency response. The proposed search algorithm, which iteratively designs filters that employ an increasing number of SPT terms, provides a means to control the filter's implementation complexity. Design examples demonstrate that our algorithm is capable of producing filters having a better frequency response than existing methods while using fewer SPT terms. We also show that the proposed algorithm can be used to design special FIR filters such as matched transmit and receive filters employing sums of signed-powers-of-two coefficients. Also presented is a modified algorithm that further reduces the required number of adders in a filter by exploiting redundancies within the coefficients.

A trellis search algorithm for the design of FIR filters with signed-powers-of-two coefficients

In this paper, an algorithm is proposed for the design of low complexity linear phase finite impulse response (FIR) filters with optimum discrete coefficients. The proposed algorithm, based on mixed integer linear programming (MILP), efficiently traverses the discrete coefficient solutions and searches for the optimum one that results in an implementation using minimum number of adders. During the searching process, discrete coefficients are dynamically synthesized based on a continuously updated subexpression space and, most essentially, a monitoring mechanism is introduced to enable the algorithm's awareness of optimality. Benchmark examples have shown that the proposed algorithm can, in most cases, produce the optimum designs using minimum number of adders for the given specifications. The proposed algorithm can be simply extended for the optimum design with the maximum adder depth constraint.

Design of Linear Phase FIR Filters With High Probability of Achieving Minimum Number of Adders

An algorithm is presented for designing digital filters with coefficients expressible as sums of signed power-of-two (SPT) terms. For each filter gain, the time complexity of the algorithm is a second-order polynomial in the filter order and is a first-order polynomial in the filter wordlength. Unlike conventional methods where each coefficient is allocated a fixed number of SPT terms, the author's method allows the number of SPT terms for each coefficient to vary subject to the number of SPT terms for the entire filter. This provides the possibility of finding a better filter without increasing the number of adders, which determines the realization cost for a given filter length. Application of the algorithm to finite impulse response (FIR) filter designs shows that it achieves up to 8.9 dB improvement over simulated annealing and mixed integer linear programing on the normalized peak ripples of example filters. >

A polynomial-time algorithm for designing digital filters with power-of-two coefficients

It is well known that if each coefficient value of a digital filter is a sum of SPT terms, the filter can be implemented without using multipliers. In the past decade, several methods had been developed for the design of filters whose coefficient values are sums of SPT terms. Most of these methods are for the design of filters where all the coefficient values have the same number of SPT terms. In this paper, we present a new method for allocating different number of SPT terms to each coefficient value keeping the total number of SPT terms fixed. Our technique yields excellent results.

Signed power-of-two (SPT) term allocation scheme for the design of digital filters

A linear time-variant (LTV) digital filter having a separable sequence as its impulse response has been proved to be recursive. Such filters have the potential of saving computation time and storage. Two techniques are presented for synthesizing a desired LTV digital filter given in numerical form in a finite time domain by a separable sequence. The first is a realization technique which decomposes the impulse response of a desired filter into a separable sequence and theoretically leads to the solution of a separable sequence with the lowest order. For a numerical solution, the order of the separable sequence is dependent on an error tolerance that reflects the realization accuracy. If the desired filter is recursive, then the exact order can be solved. The solved order, as well as the decomposition error, is independent of the error tolerance in a wide range. The second is an approximation technique which finds a separable sequence of a given order by minimizing the normalized mean squared error between the impulse response of the desired filter and the separable sequence. The technique searches the separable sequence by alternately using two nonlinear restrictions that an optimally approximated filter must satisfy. The performances of the proposed techniques are illustrated and compared with other available techniques through numerical examples. The results of the comparisons show that our approximation technique results in smaller approximation errors than those of the others. >

http://ieeexplore.ieee.org/iel4/82/6435/00251839.pdf

Finite-time-domain synthesis of recursive linear time-variant causal digital filters by separable sequences

A method is given to synthesize a desired linear time-variant (LTV) digital filter given in numerical form in a finite time domain by a separable sequence of a given order. The method finds the separate sequence by alternately using two nonlinear restrictions that an optimal recursive LTV filter approximating the desired filter must satisfy. The performance of the proposed method is illustrated and compared with other available ones through numerical examples. The results of the comparisons show that the author's method provides smaller synthesis errors than the others. >

Dongning Li

Papers

Signed power-of-two term allocation scheme for the design of digital filters

A polynomial-time algorithm for designing digital filters with power-of-two coefficients

Signed power-of-two (SPT) term allocation scheme for the design of digital filters

Finite-time-domain synthesis of recursive linear time-variant causal digital filters by separable sequences

Finite-time-domain synthesis of recursive linear time-variant causal digital filters by separable sequences