New design criterion for improving the performance of SAW bandpass digital signal processing in communication systems

This paper presents a new design criterion for improving the performance of bandpass signal processing in communication systems. The current research is a simulation and modeling of the theoretical distortionless SAW filters. The finite impulse response and the transfer function are analysed. Two methods of solutions are introduced. In the first method, the Fourier transformation based on the convolution theorem principle of the required transfer function and the convolving weighted sinc function of the window function, is explained. The second method uses the pre-envelope, complex envelope, and the conjugate theorem principle of the Fourier transformation. The transfer function is plotted for typical SAW filters with different carrier frequencies, bandwidths, and transducer lengths. The results show two conditions of the theoretical distortionless SAW devices. The first is the minimum occurring of the nonflat response in the passband (Fresnel ripples), sidelobe rejection in the stopband (Gibbs ripples) and the transition bandwidth. The second is a new criterion relating the carrier frequency and the transmission time delay of the bandpass system. This criterion is very important and should be taken into consideration during design techniques. Moreover, the transfer functions of these theoretical distortionless SAW filters are compared with that obtained by the laboratories.