Gordana Jovanovic Dolecek

Design of wideband CIC compensator filter for a digital IF receiver

This paper presents the multiplierless CIC compensation filter based on the 2M-order filter and the sharpening technique. This technique proposed by Kaiser and Hamming attempts to improve the pass band and the stop band of a symmetric nonrecursive filter using the multiple copies of the same filter. We have considered the simplest sharpening polynomial that improves the frequency characteristic with minimum increase in computational complexity. The proposed filter provides wideband compensation over the specified CIC main lobe bandwidth. The design parameter is a single integer b which depends on K, the number of cascade CIC stages and is independent on the decimation factor M. The values of b tabulated here were obtained from MATLAB simulations. A number of demonstrated characteristics make the proposed structure a good candidate for software defined radio (SDR) applications.

On MATLAB demonstrations of narrowband Gaussian noise

A demo program for teaching characteristics of narrowband Gaussian noise (NBGN) by using MATLAB environment is presented in this article. Programs are developed in MATLAB tool makeshow, and users are led step by step through the statistical characteristics of the NBGN including probability density and distribution functions, and the corresponding probability. The evaluation of the software by users is also included.

Interactive MATLAB-based demo program for sum of independent random variables

We present an interactive MATLAB‐based demo program devoted to teaching undergraduate students the behavior of the sum of independent random variables. The user chooses the type of the variables, and the parameters of these variables. The sum is shown in the time domain followed by the estimation of the probability density of the sum using a histogram. It is subsequently shown that the probability density of the sum of random variables represents the convolution of the density functions of the corresponding variables. The Central Limit Theorem and the progression of the sum towards this limit are illustrated in terms of the number of summands. The software can be used as a complement to theoretical classes or alone as a self‐study tool. Student evaluation of the program is also included.

Passband-droop compensation of modified non-recursive comb filter

This paper presents the passband-droop compensation of a modified non-recursive comb filter where the decimation factor is a power of two. The modified non-recursive comb filter is introduced to improve the alias reduction in the first folding band while keeping a low power characteristic of a non-recursive comb structure. The compensation filter is a multiplierless filter which works at low rate. The parameter of the filter depends on the cascade of filters in the last stage of the modified comb filter and does not depend on the decimation factor. In such way it is not necessary to redesign the compensation filter for new parameters.

Fractional Delay Digital Filters

The chapter goal is focused to introduce the concept of fractional delay filters (FDF), as well as a concise description of most of the existing design techniques. For this purpose, several illustrative examples are presented, where each design method is implemented by MATLAB programs. A fractional delay filter is a filter of digital type having as main function to delay the processed input signal a fractional of the sampling period time. There are several applications where such signal delay value is required, examples of such systems are: timing adjustment in all-digital receivers (symbol synchronization), conversion between arbitrary sampling frequencies, echo cancellation, speech coding and synthesis, musical instruments modelling etc. (Laakson et al., 1996). In order to achieve the fractional delay filter function, two main frequency-domain specifications must be met by the filter. The filter magnitude frequency response must have an all-pass behaviour in a wide frequency range, as well as its phase frequency response must be linear with a fixed fractional slope through the bandwidth. Several FIR design methods have been reported during the last two decades. There are two main design approaches: time-domain and frequency-domain design methods. In first one, the fractional delay filter coefficients are easily obtained through classical mathematical interpolation formulas, but there is a small flexibility to meet frequency-domain specifications. On the other hand, the frequency-domain methods are based on frequency optimization process, and a more frequency specification control is available. One important result of frequency-domain methods is a highly efficient implementation structure called Farrow structure, which allows online fractional value update. The chapter is organized as follows. Next section gives the formal definition of fractional delay filter. In the third section, some design methods are briefly described. Two efficient implementation structures for wideband fractional delay filter, as well as description of recently reported design methods for such structures, are illustrated in fourth section. MATLAB designed examples and concluding remarks are presented in fifth and sixth sections, respectively.

Application of Rouche's theorem for MP filter design

The method for the minimum-phase (MP) finite impulse response (FIR) filter design, based on Rouches theorem from complex analysis is presented here. The filter is designed directly from a given specification. The method uses the cosine filters and the sharpening technique resulting in a multiplierless filter.

Comb-Based Decimator for Multiples-of-Five Decimation Factors

This paper presents novel comb-based decimator for multiples-of-five decimation factors. The proposed decimation structure has two stages. In the first stage is a comb filter decimated by one fifth of the overall decimation factor, while in the second stage is a comb decimated by five. Additionally, the simple multiplierless filter is inserted in the second stage. This filter improves alias rejection in all folding bands except in bands which are multiples of five, in comparison with the original comb filter. Like original comb filter, the proposed filter is multiplierless.

On Design of CIC Decimators

The chapter goal is focused to introduce the concept of fractional delay filters (FDF), as well as a concise description of most of the existing design techniques. For this purpose, several illustrative examples are presented, where each design method is implemented by MATLAB programs. A fractional delay filter is a filter of digital type having as main function to delay the processed input signal a fractional of the sampling period time. There are several applications where such signal delay value is required, examples of such systems are: timing adjustment in all-digital receivers (symbol synchronization), conversion between arbitrary sampling frequencies, echo cancellation, speech coding and synthesis, musical instruments modelling etc. (Laakson et al., 1996). In order to achieve the fractional delay filter function, two main frequency-domain specifications must be met by the filter. The filter magnitude frequency response must have an all-pass behaviour in a wide frequency range, as well as its phase frequency response must be linear with a fixed fractional slope through the bandwidth. Several FIR design methods have been reported during the last two decades. There are two main design approaches: time-domain and frequency-domain design methods. In first one, the fractional delay filter coefficients are easily obtained through classical mathematical interpolation formulas, but there is a small flexibility to meet frequency-domain specifications. On the other hand, the frequency-domain methods are based on frequency optimization process, and a more frequency specification control is available. One important result of frequency-domain methods is a highly efficient implementation structure called Farrow structure, which allows online fractional value update. The chapter is organized as follows. Next section gives the formal definition of fractional delay filter. In the third section, some design methods are briefly described. Two efficient implementation structures for wideband fractional delay filter, as well as description of recently reported design methods for such structures, are illustrated in fourth section. MATLAB designed examples and concluding remarks are presented in fifth and sixth sections, respectively.

Direct Design of Infinite Impulse Response Filters Based on Allpole Filters

This chapter presents a new framework to design different types of IIR filters based on the general technique for maximally flat allpole filter design. The resulting allpole filters have some desired characteristics, i.e., desired degree of flatness and group delay, and the desired phase response at any prescribed set of frequency points. Those characteristics are important to define the corresponding IIR filters. The design includes both real and complex cases. In that way we develop a direct design method for linear-phase Butterworth-like filters, using the same specification as in traditional analog-based IIR filter design. The design includes the design of lowpass filters as well as highpass filters. The designed filters can be either real or complex. The design of liner-phase two-band filter banks is also discussed. Additionally, we discussed the designs of some special filters such as Butterworth-like filters with improved group delay, complex wavelet filters, and fractional Hilbert transformers. Finally, we addressed a new design of IIR filters based on three allpass filters. As a result we propose a new design of lowpass filters with a desired characteristic based on the complex allpole filters. Closed form equations for the computation of the filter coefficients are provided. All design techniques are illustrated with examples.

Design of Least-Square GCF compensation filter

The design of the compensation filter of a generalized comb filter (GCF) using Least-Square minimization is presented. The coefficients of the proposed compensation filter are obtained by solving two simple linear equations. The filter operates at a low rate and considerably reduces the passband droop of the GCF filter.