Low-bit Conversion & Noise Shaping
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1 Low-bit Conversion & Noise Shaping Preace Noise Shaping Mathematical basis Tricks or improving perormance Use o noise shaping pplication in D/ conversion pplication in /D conversion &<+(,('HSW+.3RO\8 2 Preace Noise shaping Expensive /D and D/ converters, laborintensive calibration procedures during manuacture, and sophisticated circuit design required to achieve the perormance and maintain it over the lie o the converter. Noise shaping can be achieved with sigmadelta modulation. s its name implies, noise shaping shits noise away rom the audio band (0 to 20 khz) thus lowering audio band noise. &<+(,('HSW+.3RO\8 3 &<+(,('HSW+.3RO\8 4
2 = 0 = 0 &<+(,('HSW+.3RO\8 5 &<+(,('HSW+.3RO\8 6 QRLVHIORRUZLWKRXW QRLVHVKDSLQJ QRLVHIORRUZLWKQRLVHVKDSLQJ Mathematical basis o 1st-order noise shaping 7KHQRLVH LQDXGLR EDQGLV JUHDWO\ UHGXFHG udio band I D LVWKHVDPSOLQJ IUHTXHQF\ 7 D &<+(,('HSW+.3RO\8 7 &<+(,('HSW+.3RO\8 8
3 7KHKLJKHUWKHRYHUVDPSOLQJ UDWHWKHPRUHWKHTXDQWL]DWLRQ QRLVHFDQEHUHPRYHGIURPWKH DXGLREDQG,WGRXEOHVWKHTXDQWL]HG QRLVHSRZHUDQGDWWKH VDPHWLPHVKLIWVWKHQRLVH WRKLJKIUHTXHQFLHV 7KHKLJKHUWKHRYHUVDPSOLQJUDWHWKHPRUHWKH TXDQWL]DWLRQQRLVHFDQEHUHPRYHGIURPWKHDXGLR EDQG udio band udio band &<+(,('HSW+.3RO\8 9 &<+(,('HSW+.3RO\8 10 The (1-1/z) actor doubles the quantized noise power and at the same time shits the noise to high requencies. The higher the oversampling rate, the more the quantization noise can be removed rom the audio band. Example: principle o operation o a 1 st - order noise shaper 7KHORFDO DYHUDJHRI WKHRXWSXW HTXDOVWR WKHLQSXW $VHTXHQFHRI IL[HGRXWSXW SDWWHUQLV JHQHUDWHGIRU DFRQVWDQWLQSXW &<+(,('HSW+.3RO\8 11 &<+(,('HSW+.3RO\8 12
4 7KHKLJKHUWKHRUGHURIWKHQRLVHVKDSHUWKH PRUHWKHTXDQWL]DWLRQQRLVHFDQEHUHPRYHG IURPWKHDXGLREDQG N th -order noise shaping could employ cascaded sections as in this 3 rd -order noise shaper. udio band &<+(,('HSW+.3RO\8 13 &<+(,('HSW+.3RO\8 14 Tricks or improving the perormance successul noise shaping circuit thus seeks to balance a high oversampling rate with noise shaping order to reduce in-band noise and shit it away rom audible range. &<+(,('HSW+.3RO\8 15 The low-level linearity o low-order noise shaping circuits can be degraded by 2 problems known as idle patterns and thresholding. zero or very low level input may result in a regular 1010 pattern. I the period o the repetition o such patterns is long enough, they may be audible as a deterministic or oscillatory tone, rather than as noise. &<+(,('HSW+.3RO\8 16
5 To remove signal distortion, a noise shaping circuit must employ dithering. Dither can be added to the input data so the circuit always operates with a changing signal even when the audio signal is zero or DC. 7KHWRWDOQRLVHSRZHULV LQFUHDVHGDVDGGLWLRQDO QRLVHLVDGGHG %XWLWFKDQJHVWKHQDWXUH RIWKHTXDQWL]DWLRQHUURU LQWRDZKLWHQRLVHZKLFK PDNHVLWPRUHLQDXGLEOH WRKXPDQ &<+(,('HSW+.3RO\8 17 &<+(,('HSW+.3RO\8 18 7KHRULJLQDOLQSXWLVDQN+]VLQXVRLGDOVLJQDO ZKLFKJHQHUDWHVDUHJXODUQRLVHSDWWHUQ 7KHQRLVHLVDXGLEOHDVWRQHV Use o noise shaping 7KHQRLVH LVDOPRVW ZKLWH DQGLVQ W DXGLEOH 7KHUHJXODU QRLVHSDWWHUQ LVUHPRYHG ZLWKGLWKHULQJ 7KHWRWDOQRLVH SRZHULVLQFUHDVHG DVGLWKHULQJ LQWURGXFHVH[WUD QRLVH Noise shaping is advantageous because a simple shaper can remove quantization noise rom the audio band. These algorithms are more eective at high sampling rates so there is more spectral space between the highest audio requency and the Nyquist requency. &<+(,('HSW+.3RO\8 19 &<+(,('HSW+.3RO\8 20
6 nother possible objective o noise shaping is reduction in the number o bits required to represent the signal. 7KLVLPSOLHVTXDQWL]DWLRQ 1RLVHVKDSLQJLVJRRGIRUTXDQWL]DWLRQ DQGKHQFHFDQEHXVHGIRUVXFKDSXUSRVH 7KHVRFDOOHGELWVWUHDPWHFKQRORJ\XVHG LQFXUUHQW&'SOD\HUVLVEDVHGRQWKLVWHFKQLTXH &<+(,('HSW+.3RO\8 21 With any 1-bit system, because o the noise shaping employed, it is diicult to quote a meaningul igure or signal-to-noise ratio because the noise level varies with respect to requency. However, in general, a 1-bit system can provide an audio-band noise loor lower than that encountered in 16- or 18-bit conversion. &<+(,('HSW+.3RO\8 22 Revisit conventional system pplication o Noise Shaping in -to-nalog Conversion s =Sampling Freq. k=no. o bits/sample Transer unction input k bit D/ Converter nalog Filter s HIIHFWRIWKH6+ s +HUHZHDVVXPHWKH FLUFXLWWRWKHVLJQDO VSHFWUXPLVQHJOLJLEOH nalog output SIGNL OPERTION SPECTRUM Summary o spectral characteristics o a conventional D/ convertion system s &<+(,('HSW+.3RO\8 24
7 Oversampling D/ system Several manuacturers have developed D/ conversion methods which employ thirdorder noise shaping. Their design details dier somewhat, particularly in the noise shaping algorithms and the low-bit output signal. The MSH system codeveloped by NTT and Matsushita is a multistage third-order noise shaping method. &<+(,('HSW+.3RO\ bit 1X input 8x oversampling digital ilter mplitude ter interpolation, higher bit-resolution is required to represent an interpolated value. 24-bit 8X 3rd-order Noise shaping 11-level 32X 1-bit 768X D/ converter (PWM+ ) Block diagram o a MSH circuit original sample interpolated sample time nalog output &<+(,('HSW+.3RO\8 26 One implementation o this design accepts 16-bit words at a nominal sampling requency, and a digital ilter stage perorms 8-times oversampling and outputs 24-bit words. Noise shaping circuits output data as an 11- value signal, at a 32-times oversampling rate. -to-analog conversion is accomplished via PWM (pulse width modulation), outputting 1-bit data at a 768- times oversampling rate. Conversion is then perormed by simply passing the 1-bit stream through a low-pass ilter. &<+(,('HSW+.3RO\8 27 &<+(,('HSW+.3RO\8 28
8 VWVWDJH VWRUGHU16FLUFXLW < ;]1 2YHUDOO < ;] 1 8x O/S ilter Noise shaping PWM+ 7ZRVWDJH FRQILJXUDWLRQ LVXVHGWR DYRLG RVFLOODWLRQ < < ]< QGVWDJH QGRUGHU 16FLUFXLW < 1 ] 1 Generally, i cascaded noise shaping circuits exceed second order they can be prone to oscillation. MSH system avoids this through its multistage coniguration. &<+(,('HSW+.3RO\8 29 &<+(,('HSW+.3RO\8 30 8x O/S ilter Noise shaping PWM+ The outputs o each stage: Y Y = 1 1 X 1 z ) = Resultant transer unction: Y = Y + ( N N1 1 z ) 1 + ( N + ( = + N z ) Y2 X (1 z ) 2 &<+(,('HSW+.3RO\ The inal element in the system is D/ conversion. The eleven-value signal is converted into pulses, each with a width corresponding to one value. This can be accomplished by applying the 4-bit output o the DSP to a ROM to map 11 amplitude values into 22 time values with constant amplitude. &<+(,('HSW+.3RO\8 32
9 %HFDXVHJUHDWWLPLQJDFFXUDF\FDQEHDFKLHYHG WKURXJKFU\VWDORVFLOODWRUVWKHZLGWKVDUHYHU\ DFFXUDWHDQGKHQFHWKHHUURURIWKHVLJQDOLVORZ Because the signal is represented by a pulse width modulation waveorm, conversion is perormed by simply passing the signal through a low-pass ilter. Because great timing accuracy can be achieved through crystal oscillators, the widths are very accurate, and hence the error o the signal is low. &<+(,('HSW+.3RO\8 33 &<+(,('HSW+.3RO\8 34 Summary s R x s Such a method achieves 20-bit resolution, but greater resolution is possible. Transer unction R x s input oversampling s s =Sampling Freq. k=no. o bits/sample R=Oversampling rate Quantization noise added Noise shaper R x s R x s Transer unction OPERTION D/ Converter nalog nalog output R x s s SIGNL SPECTRUM Summary o spectral characteristics o a oversampling D/ convertion system with noise shaping &<+(,('HSW+.3RO\8 35 &<+(,('HSW+.3RO\8 36
10 Revisit conventional system pplication o Noise Shaping in nalog-to-digital Conversion s =Sampling Freq. k=no. o bits/sample Transer unction or Signal nalog input nalog Transer unction or Signal s Quantization noise added /D Converter k bit s output OPERTION Summary o spectral characteristics o a conventional /D convertion system s SIGNL SPECTRUM &<+(,('HSW+.3RO\8 38 Oversampling /D system nalog Sigma-delta Modulation Decimation n oversampling /D converter is simple: nalog input nalog domain nalog Sigma-delta Modulation 1-bit s =Rx N domain k-bit s =Rx N Oversam pling /D conversion Decimation output k-bit N &<+(,('HSW+.3RO\8 39 The input signal is irst passed through a simple analog anti-aliasing ilter, and the input signal is sampled at a very ast rate o R to extend the Nyquist requency. The analog low-pass ilter at the input is to remove the requency components which cannot be removed by the digital ilter, but, because the preliminary sampling rate is high, the analog low-pass ilter is low order. &<+(,('HSW+.3RO\8 40
11 nalog Sigma-delta Modulation Decimation In any case, noise perormance hinges on the oversampling rate and order o noise shaping employed. The higher the order o the sigma-delta modulator we use, the lower the oversampling rate is required to achieve a given S/N perormance. &<+(,('HSW+.3RO\8 41 &<+(,('HSW+.3RO\8 42 nalog Sigma-delta Modulation Decimation,WFDXVHVOHVVKDUP HYHQWKRXJKDOLDVLQJ GRHVRFFXU The decimation process low-pass ilters the signal and noise in the 1-bit code, bandlimiting the 1-bit code prior to sample rate reduction to remove alias components. The decimation process also replaces the 1- bit coding with 16-bit coding, or example, provides a lower sampling rate, and generates a PCM output. The decimation ilter can be designed so that its requencies o maximum attenuation will coincide with the potentially aliasing requencies. comb ilter is an expedient choice because its design does not require a multiplier. &<+(,('HSW+.3RO\8 43 &<+(,('HSW+.3RO\8 44
12 In recursive orm, the transer unction o a comb ilter can be written as H 1 z z) = R ( 1 1 z Filtering is generally perormed with decimation simultaneously. 1RPXOWLSOLFDWLRQ LVLQYROYHG XQLW\FRHIILFLHQWV $JRRGEDODQFH LVUHTXLUHG &<+(,('HSW+.3RO\8 45 &<+(,('HSW+.3RO\8 46 Summary s R x s dvantages o oversampling noise shaping /D converter over conventional /D converters: It eliminates brick-wall analog ilters. It achieves increased resolution compared to SR methods by extending the spectrum o the quantization error between analog input and digital output ar outside the audio band. s =Sampling Freq, e.g khz k=number o bits/sample, e.g. 16 R=Oversampling rate Transer unction or signal R x s Summary o spectral characteristics o a oversampling /D convertion system with noise shaping Transer unction Quantization noise added R x s R x s Subsampling R x s OPERTION nalog input nalog Sigma-Delta Modulation 1 bit LDF k bit Decimation k bit R x s R x s s output s R x s R x s SIGNL SPECTRUM &<+(,('HSW+.3RO\8 47 &<+(,('HSW+.3RO\8 48
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