Compact Multiplier Research Articles

Design and analysis of a compact fast parallel multiplier for high speed DSP applications using novel partial product generator and 4 : 2 compressor

Parallel multiplier is one of the most important building blocks in all the DSP processors, which needs faster computations. To reduce the total transistor count in a multiplier we have proposed two new approaches. The first approach is using a 26 transistor booth encoder and a 8-transistor/partial-product booth selector to generate partial products. The second approach proposes a new circuit for 4 : 2 compressors. The booth encoder and booth selector reported here are the smallest in transistor count, but comparable to the best delay with less power consumption. This paper describes a comparison of a compact 16 × 16 parallel multiplier using the new circuit components. This shows a transistor count advantage of 27% and 52% in partial product generation and partial product accumulation, respectively.

A Ku-BAND WAVEGUIDE FREQUENCY MULTIPLIER USING HARMONIC-REJECTION MICROSTRIP PATCH TRANSITIONS

A compact frequency multiplier waveguide module is built by placing a planar microstrip section between two rectangular waveguides. The size of the microstrip section is minimized by eliminating all harmonic band-rejection filters. Special feed locations for the input waveguide-to-microstrip transition patches provide the second-harmonic rejection at the input, and a balanced circuit configuration formed with a pair of transistors produces the pump signal cancellation at the output. The measurements on a fully-assembled waveguide module showed a peak frequency conversion gain of-2.3 dB at 16.7 GHz with the associated output power level of 6 dBm.

Weakly compact multipliers on group algebras

We study left multipliers on the second dual spaces L 1( G)″ and M( G)″. We answer a question of Ghahramani and Lau, showing that for non-compact G a non-zero left multiplier on these spaces cannot be weakly compact.

Compactness in Wiener amalgams on locally compact groups

We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group. Our main theorem provides a generalization of the corresponding results of Feichtinger. This paper paves the way for the study of compact multiplier operators on general Wiener amalgams on the lines of Feichtinger.

Multipliers on L(S), L(S)**, and LUC(S)* for a locally compact topological semigroup

We study compact and weakly compact multipliers on L(S), L(S)**, and LUC(S)*, where the latter is the dual of LUC(S). We show that a left cancellative semigroup S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on L(S)**. We also prove that S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on LUC(S)*.

Planar Schottky diode frequency multiplier for molecular spectroscopy up to 1.3 THz

We present a novel and compact frequency multiplier design for broad-band spectroscopy up to 1.38 THz. The multiplier generates harmonics of a fundamental frequency between 110 and 240 GHz. The key element of the multiplier is a newly developed planar Schottky diode. Harmonic power generation is optimized with the aid of three tuning elements. The performance of the multiplier was checked spectroscopically.

Bounded and compact multipliers between Bergman and Hardy spaces

This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spacesA p and Hardy spacesH q. Some new characterizations of the multipliers between the spaces with exponents 1 or 2 are derived which, in particular, imply a Bergman space analogue of the Paley-Rudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixed-norm spaces, and this linkage is used to improve a known result on (A p,A 2), 1<p<2.Compact (H 1,H 2) and (A 1,A 2) multipliers are characterized. The essential norms and spectra of some multiplier operators are computed. It is shown that forp>1 there exist bounded non-compact multiplier operators fromA p toA q if and only ifp≤q.

Compact parallel multipliers using the sign-generate method in FPGA

Multiply operations are fundamental to most DSP applications. In this paper, a novel method to compute parallel multiplication in field programmable gate array (FPGA), is presented. The basic idea consists in adapting the sign-generate algorithm to the constant coefficient and the variable by variable multipliers. Implementation examples are discussed to show how to increase parallel multipliers performances, especially in density.

On compact multipliers of topological algebras

It is shown that if the maximal ideal space Δ(A) of a semisimple commutative complete metrizable locally convex algebra contains no isolated points, then every compact multiplies is trivial. In particular, compact multipliers on semisimple commutative Frechet algebras whose maximal ideal space has no isolated points are identically zero.

Multipliers and Ideals in Second Conjugate Algebras Related to Locally Compact Groups

Let G be a locally compact group. In this paper we study compact or weakly compact multipliers on the second conjugate algebras L1(G)** and M(G)**. We prove, among other things, that G is amenable if and only if there is a non-zero compact or weakly compact right multiplier on L1(G)** or M(G)**. We show that if G is σ-compact non-compact, then L1(G)** cannot have any non-zero weakly compact left multipliers T with T(n)(1) ≠ 0 for some n ∈ L1(G)**. We also study maximal regular ideals of L1(G, w) when G is a locally compact abelian group and w is a weight function on G, and Ap(G)**, 1 < p < ∞ on a locally compact group G.

Isomorphisms and multipliers on second dual algebras of Banach algebras

Suppose that A is a Banach algebra and let A be the second dual algebra of A equipped with the first Arens product 3. In this paper we characterize compact and weakly compact multipliers of A, when A possesses a bounded approximate identity and is a two sided ideal in A. We use this to study the isomorphisms between second duals of various classes of Banach algebras satisfying the above properties.

Fast and highly compact RNS multipliers

Two novel approaches are presented to the design of a fast residue number based multiplier over a Galois field GF(p), where p is a prime number. The first approach uses an isomorphic mapping from the additive index group, modulo(p—1), of GF(p) onto the direct sum of a set of submodular additive groups. The submoduli are selected for minimizing the hardware and increasing the speed. This is accomplished by fully exploiting the properties of a Galois field. The second uses symmetric residue number arithmetic to perform multiplication. This uses a pseudo-primitive root as the generator for the elements of the multiplicative group of GF(p) and reduces the index storage hardware by 50% and adder hardware by 1 bit. Multipliers designed with these approaches would be faster and use less silicon area compared to earlier designs reported in the literature.

Compact operators on a Banach space into the space of almost periodic functions

LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT5, be the translate ofT bys inS defined byT5(x)=(Tx)5. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT5.

Compact multipliers on weighted hypergroup algebras. II

In [7] we gave a description of compact multipliers of Lω(X), and left open the question of whether weakly compact multipliers on Lω(X) are compact. This had already been answered for some examples of hypergroup algebras ([1], [2], [6] and [10]). Here we give a positive answer to this question in the general setting of a weighted hypergroup algebra.

Compact multipliers on weighted hypergroup algebras

AbstractLet Mω(X) be a weighted hypergroup algebra, and Lω(X) be the Banach algebra of measures μ ε Mω(X) such that the function x ↦ (1/ω(x))δx* |μ| is norm continuous. We characterize compact multipliers on Lω(X). This extends the characterization of compact multipliers on weighted group algebras and some classes of weighted semigroup algebras.

Compactness in translation invariant Banach spaces of distributions and compact multipliers

It is shown that for a comprehensive family of translation invariant Banach spaces ( B, ∥ ∥ B ) of (classes of) measurable functions or distributions on a locally compact group (including most of the spaces of interest in harmonic analysis) the following compactness criterion generalizing the well-known results due to Kolmogorov-Riesz-Weil concerning compact sets in L p ( G), 1 ⩽ p < ∞, holds true: A closed subset M ⊆ B is compact in B if and only if it satisfies the following conditions: (a) sup ƒ ϵ M ∥ƒ∥ B < ∞; (b) ∀ ϵ > 0 ∃k ∈ K(G):∥k∗ƒ−ƒ∥ B ⩽ ϵ for all ƒ∈M; (c) ∀ϵ > 0 ∃h∈K(G):∥hƒ−ƒ∥ B ⩽ ϵ for all ƒ∈M. Among various applications a characterization of the space of all compact multipliers between suitable pairs of such spaces can be derived.

Weighted group algebra as an ideal in its second dual space

For a locally compact group G G let L 1 ( G , ω λ ) {L^1}(G,\omega \lambda ) be a weighted group algebra. We characterize compact and weakly compact multipliers on L 1 ( G , ω λ ) {L^1}(G,\omega \lambda ) . This characterization is employed to find a necessary and sufficient condition for L 1 ( G , ω λ ) {L^1}(G,\omega \lambda ) to be an ideal in its second dual space, where the second dual is equipped with an Arens product. In the special case where ω ( t ) = 1 ( t ∈ G ) \omega (t) = 1(t \in G) , we deduce a result due to K. P. Wong that if G G is a compact group, then L 1 ( G , λ ) {L^1}(G,\lambda ) is an ideal in its second dual space and its converse due to S. Watanabe.

Weakly compact operators and multipliers on C0(S, A)

The problem of defining a convolution of operator-valued measures defined on a locally compact semitopological semigroup which represent weakly compact operators is considered in this paper. Convolution of the corresponding weakly compact operators is then defined. A characterization of multipliers on function spaces is given in terms of their representing measures.

Compactness and Almost Periodicity of Multipliers

AbstractThe question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be knownIn this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.

On compact multipliers of Banach algebras

We show that if the maximal ideal space of a commutative semisimple Banach algebra B B contains no isolated points, then every compact multiplier is trivial.