Design of FIR digital filters using Semi-ellipse window

A fixed window function which is similar in shape to a semi-ellipse is proposed. The semi–ellipse which has its major axis to be equal to the window length and the minor axis at unity produced about 4.2 dB lower ripple ratio than the rectangular window. The proposed window function is derived from the equation of an ellipse in the explicit and parametric forms. First of all, the spectral characteristic of the proposed window is studied in terms of spectral parameters and compared with other fixed windows like Rectangular, Bartlett, Hann, Hamming and Blackman windows. The window simulation results reveal that the proposed window produced comparable spectral characteristic with existing standard fixed windows. Secondly, the paper presents the application of the proposed window in a digital filter design. The filter analysis comparison results with other fixed windows namely Bartlett, Von Hann, Hamming, and Kaiser window, an adjustable window, confirm that filter design with the proposed window exhibits good spectral characteristic, and can be used to design better filter than the Bartlett window using less than half the Bartlett’s filter length for a fixed transition width. The similicity of its coefficients formulation and design algorithm makes it a good choice for digital filter design applications

FIR Filter Design using Raised Semi-ellipse Window Function

In this paper, a new two-parameter window function - Raised semi-ellipse (RSE) is proposed. The window is obtained from a fixed elliptical window known as Semi-ellipse window by raising the radius of the minor axis by the parameter (β), and applied for the design of finite impulse response (FIR) digital filters. The spectral parameters of the proposed window are determined first and compared with the Kaiser window – a 2-parameter adjustable window. Subsequently, in its application in filter design with an established design algorithm, the newly proposed adjustable window is compared to the Semi-ellipse window to examine its improvement and also the Kaiser window to compare its performance with a commonly used adjustable window. The filter simulation results show that the filters designed with the proposed window can provide more reduced ripples than the Kaiser window for prescribed spectral characteristics

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Isolation Enhancement for Cylindrical Structure Millimeter-Wave Repeaters

In radio frequency (RF), microwave, and millimeter wave (mmw) repeater applications, the receiver (RX) often needs to detect small power levels while simultaneously transmitting (TX) the same signal amplified significantly without distorting the incoming signal. In some applications, this can be done with time division or frequency division duplexing techniques; however, there are full duplex repeater applications that require simultaneous transmit and receive at the same time and same frequency. These full duplex systems often face the challenge of self-interference caused by the transmitter (TX to RX isolation). This thesis focuses on enhancing the isolation between two antennas on a repeater system using different impedance surfaces. These surfaces designed to suppress the electromagnetic surface waves that propagate. For this thesis, broadband, mmw repeater systems mounted on cylinders are considered. Both numerical and analytical studies are conducted as well as fabrication and measurements are performed for cylindrical repeater applications.From a literature survey, we present a general theory on the concept of surface and generalize these impedance surfaces into three types: corrugations, pin bed, and mushroom/patch structures. Uniform depth corrugations are first considered due to their simple geometry and rich history. Theoretical approaches demonstrate how these corrugations work as an impedance surface and discuss the 2:1 frequency bandwidth limitation that is fundamental to their geometry. To overcome the bandwidth limitation, other analytical techniques are considered where the corrugations are tapered in depth such that they are engineered to choke the surface currents. This technique is shown to work consistently over wide bandwidths and is implemented onto both flat and cylinder ground planes to validate these studies and techniques. Alternatively, reactive loading of the uniform depth corrugations is shown to lead to bandwidth improvement. This eventually directs the studies to the mushroom-type impedance surfaces. These types of surfaces can be easily and accurately fabricated using printed circuit boards which can be designed on conformal substrates making them an ideal candidate for cylinder platform applications. Two types of these mushroom structures are studied in depth in this thesis and both demonstrate high isolation improvement over wide bandwidths in numerical studies and measurement results

Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function

<p/> <p>An efficient method for the design of nonrecursive digital filters using the ultraspherical window function is proposed. Economies in computation are achieved in two ways. First, through an efficient formulation of the window coefficients, the amount of computation required is reduced to a small fraction of that required by standard methods. Second, the filter length and the independent window parameters that would be required to achieve prescribed specifications in lowpass, highpass, bandpass, and bandstop filters as well as in digital differentiators and Hilbert transformers are efficiently determined through empirical formulas. Experimental results demonstrate that in many cases the ultraspherical window yields a lower-order filter relative to designs obtained using windows like the Kaiser, Dolph-Chebyshev, and Saram&#228;ki windows. Alternatively, for a fixed filter length, the ultraspherical window yields reduced passband ripple and increased stopband attenuation relative to those produced when using the alternative windows.</p