数字信号处理邵曦lecture13

1、22111111)1)(1 (1)(00zazazrezrezhjj 6.4.2 parametric resonators and equalizers simple second-order resonator:(0r1)simple parametric equalizer (参量均衡器）参量均衡器）: 22112211111111)1)(1 ()1)(1 ()(0000zazazbzbzrezrezrezrezhjjjj (10 r) (6.4.6) example 6.4.2： （： （fig. 6.4.6） rr 时的幅度频响形状不同，实现不同的功能；时的幅度频响形状不同，实现不同

2、的功能； r 和和 r 接近时，接近时，偏离偏离0的频响近似为的频响近似为 1； 零点位于单位圆时实现陷波。零点位于单位圆时实现陷波。 a notch filter(陷陷波波滤滤波波器器) with two notch frequencies 0: )1)(1 ()1)(1 ()(11110000zrezrezezezhjjjj)()(1zrnzn 6.4.3 notch and comb filters a notch filter with notches at arbitrary (finite) set of frequencies m1: )()()1 ()1 ()(11111znz

3、nzezezhmijmijii mmmmmzbzbzbzb111111（6.4.9） 1 作用：作用：)(h remains flat except in the vicinity of the notch frequencies. example 6.4.3：a dsp system,sf600hz, is plague by 60hz power frequency interference (工工频频干干扰扰) noise and its harmonics (谐谐波波). design a notch filter to remove all the harmonics but rem

4、ains flat at other frequencies. solution： 首先确定要陷波的干扰频率首先确定要陷波的干扰频率： 基频基频2 . 0211sff 假 设 采 样 前 无 预 滤 波 ， 采 样 后 ， 工 频 干 扰 谐 波 频 率 为假 设 采 样 前 无 预 滤 波 ， 采 样 后 ， 工 频 干 扰 谐 波 频 率 为)2mod()2 . 0(i), 2, 1(i，即，即2 . 0 ii)90( i。 这就是陷波器要滤去的这就是陷波器要滤去的 10 个频率。个频率。 其次，设计陷波器其次，设计陷波器： h(z)应以应以ije)90( i为零点，它们正好是单位圆的为零

5、点，它们正好是单位圆的 10 等分等分点，即点，即101 z的的 10 个根。个根。 （ijijee2 . 01012101)(1） 10101011)(zzzh 取取1如如0.9980，以使频响在陷波频率处尖锐，在其他频，以使频响在陷波频率处尖锐，在其他频率处平坦（率处平坦（p.256 figurecomb-like frequency response） peaking filter: if we move the notch zeros into the unit circle and behind the poles, the notching filter will convert

6、to a peaking filter. (p.257) mmmmmmmijmijzbzbzbrzrbznzrnzezrezhii111111111111)()()1 ()1 ()( (r) （6.4.10） （ n(z) 仍仍是是指指mmmijzbzbzei11111)1 (） example 6.4.5：2020202011)(zzrzh ， r zeros: ：ijijreerrz20220122020120)()(，190i poles: ijez202，190i if 1 and r，| )(|h exhibits sharp peaks at i202（190i）and remai

7、ns flat except in the vicinity of these frequencies. (p.258, figure) notching filter (6.4.9) comb filters(梳梳状状滤滤波波器器). peaking filter (6.4.10) notching comb filters are typically used to cancel periodic interference (去去除除周周期期性性干干扰扰). peaking comb filters are often used to enhance periodic signals (周

8、周期期性性信信号号的的增增强强) in noise. convolution for lsi filtering: )(*)()(nhnxny (6.5.1) deconvolution (解卷积解卷积): recover x(n) from y(n) and h(n) inverse filtering (逆滤波逆滤波): filtering y(n) through the inverse filter y(n) )(1)(zhzhinv (6.5.2) x(n) output: )()(1)()()(1)(zxzhzhzxzhzy or )(*)()(nhnynxinv (6.5.3)

9、6.5 deconvolution, inverse filters and stability application 1：channel equalization (信信道道均均衡衡)，fig.6.5.2 application 2： digital audio effects (数数字字音音效效) （p. 260） remove the local reverberation (混混响响) effects of a room, and add the reverberation ambience of a concert hall that increases the warmth an

10、d richness of the sound. (fig.6.5.3) x(n) )(1zhroom )(zhhall )(zhroom )(nyhall dsp processor（prefiltering） 解解卷卷积积输输出出与与 x(n)有有误误差差，可可能能的的来来源源: determination of )(zhinv y(n) is contaminated with noise： )()(*)()(nvnhnxny (6.5.6) the deconvolution of the noisy y(n): )( )()(*)()()(*)()( nvnxnvnhnxnynhnx

11、invinv (6.5.7) if )(nhinv has an infinite anticausal part, the clipping approximation will cause deconvolution error. (will be discussed below) the zeros and poles of )(zh are the poles and zeros of )(zhinv; the stability of )(zhinvis more crucial than the causality. 关于逆系统的因果、稳定性：关于逆系统的因果、稳定性： assum

12、e )(zh is stable and causal the poles lie strictly inside the unit circle. ( i) if the zeros of )(zh also lie inside the unit circle, the stable )(nhinv is causal. (ii) if the zeros of )(zh lie outside the unit circle, the stable )(nhinv is anticausal. handling the stable and anticausal inverse filter: using the clip/delay approximation technique (p.119120 ) )()()(,nhnhnhdinvdelayinvclipinv 如何使用无限长非因果逆滤波器：如何使用无限长非因果逆滤波器： clip the infinite anticausal tail of )(nhinv： dndnnhnhinvinv0)()( (6.5.8) the deconvolution error arising from the clipped filter: 1)()()()()()(*)()()()(dminvmin