All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples

Filtration and Synthesis of Different types of Human Voice Signals: An application of digital signal processing

An observation of the effect in audio signal by using digital filter plays an important role in the field of digital signal processing (DSP). Day by day the digital form of signal is becoming more preferable than the analog one which is increasing the need of DSP in the rapidly changing world. Yet, there are many attractive schemes for designing a digital filter; we adopt windowing technique for design a FIR low pass filter in the frequency domain for the short period. However, the main task of our work is to perform filtration of the different types of practical human voice signals by using digital filter and synthesis of those signals to reduce the memory size (kB) by remaining the same quality of the signal. We used MATLAB for the design of digital filter and synthesis of those audio signals. MATLAB provides different options for signal synthesis. Finally, this paper gives an idea about reconstructed signals and filtrated signals. Keywords: Digital filter, Cutoff frequency, Fourier transform, Inverse Fourier transforms, normalized frequency

Spectral analysis of randomly sampled signals: suppression of aliasing and sampler jitter

Nonuniform sampling can facilitate digital alias-free signal processing (DASP), i.e., digital signal processing that is not affected by aliasing. This paper presents two DASP approaches for spectrum estimation of continuous-time signals. The proposed algorithms, named the weighted sample (WS) and weighted probability (WP) density functions, respectively, utilize random sampling to suppress aliasing. Both methods produce unbiased estimators of the signal spectrum. To achieve this effect, the computational procedure for each method has been suitably matched with the probability density function characterising the pseudorandom generators of the sampling instants. Both proposed methods are analyzed, and the qualities of the estimators they produce have been compared with each other. Although none of the proposed spectrum estimators is universally better than the other one, it has been shown that in practical cases, the WP estimator produces generally smaller errors than those obtained from WS estimation. A practical limitation of the approaches caused by the sampling-instant jitter is also studied. It has been proven that in the presence of jitter, the theoretically infinite bandwidths of WS and WP signal analyses are limited. The maximum frequency up to which these analyses can be performed is inversely proportional to the size of the jitter

Moving and stationary target acquisition radar image enhancement through polynomial windows

The Fourier transform involved in synthetic aperture radar (SAR) imaging causes undesired sidelobes which obscure weak backscatters and affect the image clarity. These sidelobes can be suppressed without deteriorating the image resolution by smoothing functions known as windowing or apodization. Recently, the theory of orthogonal polynomials has gained considerable attention in signal processing applications. The window functions that are derived from the orthogonal polynomials have interesting sidelobe roll-off properties for better sidelobe apodization, hence it can be used for radar image enhancement. In this work, a new window is constructed from Jacobi orthogonal polynomials and its performance in SAR imaging is analyzed and compared with commonly used window functions. Also, apodization functions involved in Fourier transform harmonic analysis and Fourier transform spectroscopy are discussed in the context of SAR imaging