Goran Molnar

Closed-Form Design of CIC Compensators Based on Maximally Flat Error Criterion

The simplest decimation filter is the cascaded-integrator-comb (CIC) filter. However, its magnitude response has a high passband droop, which is not tolerable in many applications. One technique for the reduction of the droop is the compensation by a filter called CIC compensator. This brief presents a method for the design of high-order finite-impulse-response CIC compensators which is based on maximally flat error criterion. The compensators coefficients are obtained by solving a linear system of equations, which is formed using a straightforward procedure. The compensators presented are suitable for application in narrow-band software radio receivers.

Noncausal IIR Fractional Hilbert Transformers With Equiripple or Flat Phase Response

Noncausal infinite impulse response (IIR) systems yield a much better approximation of desired response than causal systems of the same complexity. Todays technology also enables their efficient implementation. In the design of Hilbert transformers, the noncausal approach has been exploited only for conventional transformers. This brief presents a method for the design of noncausal IIR fractional Hilbert transformers based on the elliptic approximation of the desired phase shift. All-pass transformers with equiripple and flat phase responses are considered. The method is given in closed form, which makes the design robust and suitable for high-order transformers.

FPGA implementation of high-frequency software radio receiver

State-of-the-art analog-to-digital converters allow the design of high-frequency software radio receivers that use baseband signal processing. However, such receivers are rarely considered in literature. In this paper, we describe the design of a high-performance receiver operating at high frequencies, whose digital part is entirely implemented in an FPGA device. The design of digital subsystem is given, together with the design of a low-cost analog front end.

Bernoulli Low-Pass Filters

Selective filters are obtained by the approximation of the rectangular magnitude. Classic approximation methods employ polynomials or rational functions. Modern methods are based on numerical optimization. The optimization-based approach is effective and gives the designer much freedom. However, the polynomial methods are still attractive because they result in closed-form expressions and simple design procedures. This brief presents a class of low-pass filters that approximate the rectangular magnitude by using the Bernoulli polynomials. The presented filters have equiripple magnitude responses in the lower parts of the passbands, nonequiripple responses at the frequencies approaching the cutoff, and steep transition bands. Furthermore, they have low quality factors of the poles.

Time-Domain Synthesis of Continuous-Time Systems Based on Second-Order Cone Programming

A method for the design of continuous-time systems approximating prescribed impulse response is presented. The method is based on the least-squares error criterion. Using zero-pole-gain representation of the system, a constrained optimization problem is formed. The optimum is found by iterative procedure in which a second-order cone program is solved in each iteration. The method is applied in the design of continuous-time wavelet filters and high-voltage pulse-forming networks. It proved to be fast with low sensitivity to the iteration starting-point. Furthermore, it is suitable for the design of high-order systems.

Design of multiplierless CIC compensators based on maximum passband deviation

Cascaded-integrator-comb (CIC) decimation filters are the simplest multiplierless filters supporting high sample rate conversion factors. However, the magnitude response of high order CIC filters exhibits a high passband droop. Such a droop can be reduced by connecting an FIR compensator in the cascade with the CIC filter. In this paper, we present a method for the design of CIC compensators whose coefficients are expressed as a sum of powers of two (SPT). The method is based on the minimization of the difference between the maximum and the minimum passband amplitude. To obtain the compensator coefficients, we use a global optimization technique, which is based on the interval analysis. In the optimization, the number of SPT terms for each coefficient is specified. The compensators obtained efficiently compensate narrow and wide passbands by using three and five coefficients having small number of SPT terms. For these compensators, multiplierless structures are provided.

FIR fractional Hilbert transformers with raised-cosine magnitude response

Fractional Hilbert transformers find applications in communications and image processing. Various methods have been developed for their design. Some of them start from previously designed conventional Hilbert transformer, whereas others perform the design directly. In this paper, we present a closed-form method for the design of FIR fractional Hilbert transformers, which is based on well-known Fourier series method. The presented method results in transformers whose transfer functions approximate raised-cosine magnitude response with fractional phase shift in the least-squares sense. We used such frequency response because the corresponding impulse response is well localized in time, what enables the use of the Fourier series method without additional window function. The features of the proposed transformers are illustrated by examples which include the design of fractional and conventional transformers as well as complex Hilbert filters.

Design of Systems with Prescribed Impulse Response Based on Second-Order Cone Programming

A method for the design of continuous-time systems approximating prescribed impulse response is presented. The design uses weighted least squares criterion, which is applied in the time domain. The method is developed based on iterative procedure solving a second-order cone programming (SOCP) subproblem in each iteration. It supports design criteria such as stability and minimum phase. Features of the proposed method are illustrated with a design of pulse-shaping filter for ultra-wideband (UWB) transmission systems.

Time-domain distortion as criterion for design of IIR Hilbert transformers

The ideal Hilbert transformer can be defined as the system with unity magnitude and odd-symmetric impulse response. Based on this definition, the measure for time-domain distortion of transformed signal is defined. The measure is suitable for the design as well as for the comparison of the IIR all-pass Hilbert transformers. These applications are illustrated by examples, which consider the relationship between the transformers designed in the frequency domain and the transformers obtained by minimization of the proposed measure. It is shown that, under certain conditions, the least-squares approximation is suboptimal in the sense of time-domain distortion.

Spectral-efficient UWB pulse shapers generating Gaussian and modified Hermitian monocycles

Ultra-wideband (UWB) impulse radio uses very short pulses whose spectra are regularized by Federal Communications Commission (FCC). One technique to obtain these pulses is shaping. The shaping is realized with a bandpass filter called pulse shaper. Its impulse response approximates an FCC-compliant waveform. In this paper, we propose spectral-efficient shapers whose responses approximate high-order Gaussian and modified Hermitian monocycles. To obtain the optimum shapers, we use leasts-quares error criterion. Furthermore, for various orders of monocycles, we provide the transfer functions that exhibit high spectral efficiency. Within the FCC UWB passband, the transfer functions of the Gaussian shapers ensure the spectral efficiency up to 89%, whereas the functions of the modified-Hermitian shapers provide the efficiency up to 62%.