信号处理导论（英）8.3 Noise Reduction and Signal Enhancement.pptVIP

8.3 Noise Reduction and Signal Enhancement * * 信号处理的一个重要的、常见的目的就是从混有噪声的信号中提取有用信号。 Fig.8.3.2 （信号在白噪声中，做的是第二种选择） 既然不能完全去除噪声，就要有指标衡量去除噪声的程度。 1) NRR(noise reduction ratio)： The NRRs computed in Eqs (8.3.6) or ( 8.3.7) give the maximum noise reductions achievable with ideal lowpass or bandpass filters that do not distort the desired signal 2) SNR(signal-to-noise ratio) 上述理想滤波器是不能实际实现的（because they have double-sided impulse responses with infinite anticausal tails）。实际的滤波器不会有那么陡峭的过渡带性能（sharp transient characteristic）。 实际中用滤波器去除噪声，必须考虑以下两个问题： 1) transient response of filter The more closely a filter approximates the sharp transient characteristics of an ideal response , the closer to the unit circle its poles get,and the longer its transient response becomes. Stated differently ,maximum noise reduction .approaching the ideal limit (8.3.6) ,can be achieved only at the expense of introduction long transients in the output . 2) the amount of delay introduced into the output The issue of the delay introduced into the output has to do with the steady-state response of the filter .We recall from Eq.(6.3.8) of Chapter 6 that after steady state has set in ,different frequency components of an input signal suffer different amounts of delay ,as determined by the phase delay of the filter . 下面我们看几个用简单的滤波器去噪的例子，计算滤波器的去噪比，并讨论去噪与暂态响应时间的矛盾。 Example 8.3.1: Example 8.3.2 : Example 8.3.3 : First-order IIR smoother with prescribed cutoff frequency The NRR of Example 8.3.1 can be improved slightly , without affecting the speed of response ,by adding a zero in the transfer function at z=－1 .or The zero at suppresses the high-frequency portion of the input noise spectrum even more than the filter of Example 8.3.1 Example 8.3.4: FIR averaging filters 用FIR DF 实现去除低频信号中混杂噪声 The optimum length-N FIR filter with unity DC gain and maximum NRR is: How does the FIR smoother compare with the IIR smoother of Example 8.3.1？ 1) IIR is very simple compu