數(shù)字信號處理邵曦lecture23

1、chapter 8 signal processing applications8.1 digital waveform generators f filtering approach design a filter h(z) whose impulse response h(n) is the waveform to be generated. input and get the desired waveform at the output. disadvantage: require a certain amount of computational overhead(額外的計算開銷額外的

2、計算開銷)(n wavetable synthesis (波表合成）波表合成） precompute the waveform samples, store them in a table in ram. access the table in a controlled way. 8.1.1 sinusoidal generators to generate a (causal) sinusoidal signal of frequency 0, the filter will be: )()sin()(0nunrnhn 21010cos21sin)(2)()(00zzrzrnujeerzzh

3、njnjn (8.1.1) second-order system, canonical form (fig.8.1.1) example 8.1.1： an application of sinusoidal generator：touchtone (全全數(shù)數(shù)字字按按鍵鍵式式) or dtmf (雙雙音音多多頻頻) transmitter/receiver transmitting end： each key-press on the keypad generates the sum of two audible sinusoidal tones. )cos()cos()(nnnyhl (f

4、ig.8.1.3, fig.8.1.4) receiving end： detect which pair of frequency ,hl is present by filtering y(n) through a bank of bandpass filters (帶通濾波器組帶通濾波器組 ) or by computing the dft of y(n). 8.1.2 periodic waveform generatorsabout periodic sequence(周期序列）周期序列）: a periodic analog signal does not necessarily

5、remain periodic after sampling. a sinusoid x(t) with frequency f produces periodic x(n) only when some condition about f and the sampling rate fs is satisfied. periodic waveform generator: consider a sequence of period d=4, the impulse response of the filter is: )(32103210bbbbbbbbnh 4332211084332211

6、073625140332211001)1)()()(zzbzbzbbzzzbzbzbbzbzbzbzbzbzbzbbznhzhnn (8.1.11) to generate a sequence of period d, the filter is dddzzbzbbzh1)() 1(1110 (8.1.10) 8.2 digital audio effects 8.2.1 delays, echoes and comb filters single reflection or echo (回聲回聲) ) filter )()()(dnaxnxny 1|a (8.2.1) dazzh1)( ，

7、 )()()(dnannh （8.2.2） successive echoes )3()2()()()(32dnxadnxadnaxnxny （8.2.8） dddddazzazazaazzh111)(443322 (8.2.9) dddddazzazazaazzh111)(443322 (8.2.9) zeros：44azd， but azd ) 10() 140(21421dkeazdkeazdkjddkjd ) 10,4, 140(421dmmkdkeazdkjd zeros pattern and comb-like response (fig.8.2.5) plain reverbe

8、rator(混響器混響器) adding up infinite number of successive echoes imitates the reverberation in a room: )2()()()(2dnxadnaxnxny （8.2.10） dddazzaazzh111)(22 (8.2.12) )()()(nxdnayny (8.2.13) poles: ) 10(21dkeazdkjd poles pattern and comblike response (fig.8.2.7) effective time constant : daandefflnln)ln(lnlnln1 tadtneffefflnln (8.2.16) allpass reverberator： ddazzazh1)( (8.2.25) 1| )(|h ididzabaazbazh)(1)(0