Patent ID: 7376688
Filing Date: 2008-05-20
Classification: G06F,H04L

Abstract:
1. A least-squares method for generating and applying Wavelet waveforms and filters, said method comprising the steps: said Wavelet is a digital finite impulse response waveform at baseband in the time domain, linear phase finite impulse response filter requirements on the passband and stopband performance of the power spectral density are specified by linear quadratic error metrics in the Wavelet, Wavelet requirements on the deadband for quadrature mirror filter properties required for perfect reconstruction are specified by a linear quadratic error metric in the Wavelet, Wavelet orthogonality requirements for intersymbol interference and adjacent channel interference are specified by non-linear quadratic error metrics in the Wavelet, non-linear quadratic error metrics have quadratic coefficients dependent on the Wavelet, Wavelet multi-resolution property requires said error metrics to be converted to error metrics in the discrete Fourier transform harmonics of the Wavelet which harmonics are the Wavelet impulse response in the frequency domain, using a least-squares recursive solution algorithm with quadratic error metrics, which algorithm requires a means to find the Wavelet harmonics that minimize the sum of said linear quadratic error metrics, said harmonics are used to linearize said non-linear quadratic error metrics, said least-squares recursive solution algorithm finds the harmonics which minimize the weighted sum of the linear and linearized quadratic error metrics, said least-squares recursive solution algorithm starts over again by using said harmonics to linearize the non-linear error metrics and to find the corresponding harmonics which minimize the sum of said linear and linearized quadratic error metrics, said least-squares recursive solution algorithm continues to be repeated until the solution converges to the design harmonics of the Wavelet which is the least-squares error solution, and said Wavelet impulse responses in the time domain and frequency domain are implemented in communication systems for waveforms and filters.