Two discrete-time Wirtinger-type inequalities relating the power of a finite-length signal to that of its circularly-convolved version are developed. The usual boundary conditions that accompany the existing Wirtinger-type inequalities are relaxed in the proposed inequalities and the equalizing sinusoidal signal is free to have an arbitrary phase angle. A measure of this sinusoidal signal's power, when corrupted with additive noise, is proposed. The application of the proposed measure, calculated as a ratio, in the evaluation of the power of a sinusoid of arbitrary phase with the angular frequency π/N, where N is the signal length, is thoroughly studied and analyzed under additive noise of arbitrary statistical characteristic. The ratio can be used to gauge the power of sinusoids of frequency π/N with a small amount of computation by referring to a ratio-versus-SNR curve and using it to make an estimation of the noise-corrupted sinusoid's SNR. The case of additive white noise is also analyzed. A sample permutation scheme followed by sign modulation is proposed for enlarging the class of target sinusoids to those with frequencies M π/N, where M and N are mutually prime positive integers. Tandem application of the proposed scheme and ratio offers a simple method to gauge the power of sinusoids buried in noise. The generalization of the inequalities to convolution kernels of higher orders as well as the simplification of the proposed inequalities have also been studied.

This letter describes theoretical characteristics of the electron diffraction transistor and its inverter circuit. The electron wave diffraction due to a transverse potential grating is analyzed taking thermally induced dispersions into account. The switching time is estimated as 0.4 ps at 77 K.

In practical applications of digital filters it is more realistic to treat multiplier coefficients as finite intervals than restricting them to infinite or very long word-length representations. However, this can not be done it the frequency response performance under interval assumption is difficult to analyze. In this paper, it is proved that stable lattice allpass filters possess bounded continuous phase response when lattice parameters vary in bounded intervals. It is shown that sharp bounds on the interval phase response can be computed easily at an arbitrary frequency using a simple recursive procedure. Application of this property to the problem of finite word-length lattice allpass filter design is also discussed. By formulating this problem as an interval design it is possible to solve it efficiently independent of the number system used to represent multiplier coefficients.

It is shown that two-dimensional linear phase FIR digital filters with various shapes of frequency response can be designed and realized as modular array structures free of multiplier coefficients. The design can be performed by judicious selection of two low order linear phase transfer functions to be used at each module as kernel filters. Regular interconnection of the modules in L rows and K columns conditioned with boundary coefficients 1, 0 and 1/2 results in higher order digital filters. The kernels should be chosen appropriately to, first, generate the desired shape of frequency response characteristic and, second, lend themselves to multiplierless realization. When these two requirements are satisfied, the frequency response can be refined to possess narrower transition bands by adding additional rows and columns. General properties of the frequency response of the array are investigated resulting in Theorems that serve as valuable tools towards appropriate selection of the kernels. Several design examples are given. The array structures enjoy several favorable features. Specifically, regularity and lack of multiplier coefficients makes it suitable for high-speed systolic VLSI implementation. Computational complexity of the structure is also studied.

The group-delay sensitivity is studied theoretically for Gray and Markel allpass lattice filter realizing complex transfer function. Recursive expressions which were derived for phase and group-delay in real lattice are rederived for the complex case. These expressions are used to obtain upper bounds on group-delay sensitivity. The minimum number of frequencies where group-delay sensitivity becomes zero is discussed. Results corresponding real allpass lattice are also shown. Phase sensitivity properties of these filters are analyzed and compared with existing results. A new bound on phase sensitivity is also obtained.

An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.

A classs of type 1 linear phase FIR digital filters is proposed. The filter can be realized using a parallel, modular and regular array structure. It is shown that, under some simple constraints, the consisting modules of the array can be realized free of multiplier coefficients. Such two dimensional mesh arrays are specially suitable for realization with special-purpose systolic hardware for high-speed digital signal processing tasks. Compared to the array structure, proposed by the authors, for multiplierless realization of maximally flat FIR digital filters, this class needs less adders to fulfill the same magnitude response requirements. Another attractive property of the proposed array is that a number of highpass or lowpass filters with different passband widths can be realized simultaneously in a very economical way.

As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system. An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient. In this paper, the eigensignals are studied and characterized in the time and z domains. The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambert-form series are used for the transform-domain characterization. Examples of non-trivial eigensignals are provided. These include the special classes of multiplicative and completely multiplicative eigensignals. Moreover, the locus of poles of eigensignals with rational z transforms are identified.

In this paper we propose a method for increasing the reliability in multiprocessor realization of lowpass and highpass FIR digital filters possessing a maximally flat magnitude response. This method is based on the use of array realization of the filter which has been proposed earlier by the authors. It is shown that if a processing module of the array functions erroneously, it is possible to exclude the module and still obtain a lowpass FIR filter. However, as a price we should tolerate a slight degradation in the magnitude response of the filter that is equivalent to a wider transition band. We also analyze the behavior of the filter when our proposed schemes are implemented on more than one module. The justification of our approach is based on that a slight degradation of the spectral characteristics of a filter may be well tolerated in most filtering applications and thus a graceful degradation in the frequency domain can sufficiently reduce the vulnerability to errors.

The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.