边带信号1-(精品课件).ppt

* Representation:表示，代表 characterization:描述 performance:性能，特性 convergence:收敛 response:响应 detection:检测 distortion:失真，变形 criterion:准则 predictive:预测性的 algorithm:算法 estimate:估值 recursive:递归的 adaptive:匹配 blind:盲的 maximum-likelihood：最大似然 Some useful words Representation of the bandpass signals Fourier transform The function g(t) is Fourier transformable if the following condition is fulfilled Some notations: ?=2?f or By using Fourier transform, the time domain signal g(t) is expressed as a continuous sum of exponential function with frequencies in the interval -? to ?. The Fourier transform of signal defines the frequency-domain representation of the signal. The signals can be defined by either the time domain or frequency domain representation. Example: rectangular function In general, the Fourier transform G(f) is a complex function of frequency f, so that we may express it in the form is amplitude spectrum, and ?(f) is phase spectrum For the real valued signal g(t), we have *: the complex conjugate That is For the real valued signal 1. The amplitude spectrum is an even function of frequencies. That is the amplitude is symmetric about the vertical axis. 2. The phase of the signal is an odd function of the frequency. That is the phase spectrum is anti-symmetric about the vertical axis. Hilbert transform: To shift the phase angle of the given signal by ?90o Assume a filter with response function of This filter produce a phase shift of -90 degrees for all the positive frequencies of the input signal and +90 degrees for all the negative frequencies f Phase of H(f) +90? -90? The Hilbert transform pair: is the Hilbert transform of g(t) The Hilbert transform shifts the phase of the signal spectrum by ?90 degrees. Assume the passband signal s(t) is real valued. Now we need to derive the mathematical representation of s(t) fc -fc S(f) Therefore we have fc -fc jS(f) We define the pre-envelope of the signal s(t) as s+(t) The s+(t) has the positive spectrum fc -fc S+(f) There