Apparatus and method for performing properrizing frequency shift(p-FRESH) vectorizing

摘要

To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described herein, there is provided a method for performing properizing frequency shift (p-FRESH) vectorizing, the method comprising: converting a scalar-valued input signal of length L into a 2L-by-1 vector-valued output signal including complex conjugate signal of the input signal; modulating the input signal and the complex conjugate signal each with L different carriers; and bandpass filtering the modulated signal to form the output signal, wherein the output signal is band-limited to a half-Nyquist zone (F+).

主权项

1. A method for performing properizing frequency shift (p-FRESH) vectorizing, the method comprising:
converting a scalar-valued input signal into a 2L-by-1 vector-valued signal including L signals of the input signal and L complex conjugate signals of the input signal, wherein L is an integer; modulating the 2L-by-1 vector-valued signal with L different carriers by modulating each of the L signals and the L complex conjugate signals with the L different carriers; bandpass filtering the modulated 2L-by-1 vector-valued signal to form an output signal; and transmitting the output signal, wherein the output signal is defined by a following expression:Yl⁡(t)={(X⁡(t)⁢ⅇ-2⁢⁢j⁢⁢π⁢⁢fl⁢t)*g⁡(t),for⁢⁢l≤L(X⁡(t)*⁢ⅇ-2⁢⁢j⁢⁢π⁢⁢fl-L⁢t)*g⁡(t),for⁢⁢l>L, where t denotes time, fl denotes center frequency of an l-th Nyquist zone, X(t) is the input signal, X(t)* is the conjugation of the input signal, g(t) is the impulse response bandpass filtering a half-Nyquist zone(F+), Yl(t) is the output signal, and l=1, 2, . . . , 2L.