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Low-Bit Conversion & Noise Shaping

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Low-Bit Conversion & Noise Shaping Low-bit Conversion ■ Preface & ■ Noise Shaping Noise Shaping ■ Mathematical basis ■ Tricks for improving performance ■ Use of noise shaping ■ Application in D/A conversion ■ Application in A/D conversion &<+(,('HSW+.3RO\8 2 Preface Noise shaping ■ Expensive A/D and D/A converters, labor- ■ Noise shaping can be achieved with sigma- intensive calibration procedures during delta modulation. manufacture, and sophisticated circuit ■ As its name implies, noise shaping shifts design required to achieve the performance noise away from the audio band (0 to 20 and maintain it over the life of the kHz) thus lowering audio band noise. converter. &<+(,('HSW+.3RO\8 3 &<+(,('HSW+.3RO\8 4 = 0 = 0 &<+(,('HSW+.3RO\8 5 &<+(,('HSW+.3RO\8 6 QRLVHIORRUZLWKQRLVHVKDSLQJ QRLVHIORRUZLWKRXW Mathematical basis of 1st-order QRLVHVKDSLQJ noise shaping 7KHQRLVH LQDXGLR EDQGLV JUHDWO\ UHGXFHG Audio band IDLVWKHVDPSOLQJ IUHTXHQF\ 7D &<+(,('HSW+.3RO\8 7 &<+(,('HSW+.3RO\8 8 7KHKLJKHUWKHRYHUVDPSOLQJ ,WGRXEOHVWKHTXDQWL]HG UDWHWKHPRUHWKHTXDQWL]DWLRQ QRLVHSRZHUDQGDWWKH 7KHKLJKHUWKHRYHUVDPSOLQJUDWHWKHPRUHWKH QRLVHFDQEHUHPRYHGIURPWKH VDPHWLPHVKLIWVWKHQRLVH TXDQWL]DWLRQQRLVHFDQEHUHPRYHGIURPWKHDXGLR DXGLREDQG WRKLJKIUHTXHQFLHV EDQG Audio band Audio band &<+(,('HSW+.3RO\8 9 &<+(,('HSW+.3RO\8 10 ■ Example: principle of operation of a 1st- ■ The (1-1/z) factor doubles the quantized order noise shaper $VHTXHQFHRI noise power and at the same time shifts the IL[HGRXWSXW noise to high frequencies. 7KHORFDO SDWWHUQLV DYHUDJHRI JHQHUDWHGIRU ■ The higher the oversampling rate, the more WKHRXWSXW DFRQVWDQWLQSXW the quantization noise can be removed from HTXDOVWR the audio band. WKHLQSXW &<+(,('HSW+.3RO\8 11 &<+(,('HSW+.3RO\8 12 7KHKLJKHUWKHRUGHURIWKHQRLVHVKDSHUWKH PRUHWKHTXDQWL]DWLRQQRLVHFDQEHUHPRYHG IURPWKHDXGLREDQG ■ Nth-order noise shaping could employ cascaded sections as in this 3rd-order noise shaper. Audio band &<+(,('HSW+.3RO\8 13 &<+(,('HSW+.3RO\8 14 Tricks for improving the performance ■ A successful noise shaping circuit thus ■ The low-level linearity of low-order noise seeks to balance a high oversampling rate shaping circuits can be degraded by 2 with noise shaping order to reduce in-band problems known as idle patterns and noise and shift it away from audible range. thresholding. ■ A zero or very low level input may result in a regular 1010 pattern. If the period of the repetition of such patterns is long enough, they may be audible as a deterministic or oscillatory tone, rather than as noise. &<+(,('HSW+.3RO\8 15 &<+(,('HSW+.3RO\8 16 7KHWRWDOQRLVHSRZHULV %XWLWFKDQJHVWKHQDWXUH LQFUHDVHGDVDGGLWLRQDO RIWKHTXDQWL]DWLRQHUURU QRLVHLVDGGHG LQWRDZKLWHQRLVHZKLFK PDNHVLWPRUHLQDXGLEOH WRKXPDQ ■ 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. &<+(,('HSW+.3RO\8 17 &<+(,('HSW+.3RO\8 18 7KHRULJLQDOLQSXWLVDQN+]VLQXVRLGDOVLJQDO ZKLFKJHQHUDWHVDUHJXODUQRLVHSDWWHUQ Use of noise shaping 7KHQRLVHLVDXGLEOHDVWRQHV ■ 7KHUHJXODU Noise shaping is advantageous because a QRLVHSDWWHUQ simple shaper can remove quantization LVUHPRYHG 7KHQRLVH noise from the audio band. ZLWKGLWKHULQJ LVDOPRVW ■ These algorithms are more effective at high ZKLWH DQGLVQ·W 7KHWRWDOQRLVH sampling rates so there is more spectral DXGLEOH SRZHULVLQFUHDVHG space between the highest audio frequency DVGLWKHULQJ and the Nyquist frequency. LQWURGXFHVH[WUD QRLVH &<+(,('HSW+.3RO\8 19 &<+(,('HSW+.3RO\8 20 ■ Another possible objective of noise shaping ■ With any 1-bit system, because of the noise is reduction in the number of bits required shaping employed, it is difficult to quote a to represent the signal. meaningful figure for signal-to-noise ratio 7KLVLPSOLHVTXDQWL]DWLRQ because the noise level varies with respect to frequency. 1RLVHVKDSLQJLVJRRGIRUTXDQWL]DWLRQ ■ However, in general, a 1-bit system can DQGKHQFHFDQEHXVHGIRUVXFKDSXUSRVH provide an audio-band noise floor lower than that encountered in 16- or 18-bit 7KHVRFDOOHGELWVWUHDPWHFKQRORJ\XVHG LQFXUUHQW&'SOD\HUVLVEDVHGRQWKLVWHFKQLTXH conversion. &<+(,('HSW+.3RO\8 21 &<+(,('HSW+.3RO\8 22 Revisit conventional system Digital input f =Sampling Freq. Application of Noise Shaping in s A k bit +HUHZHDVVXPHWKH k=No. of bits/sample fs HIIHFWRIWKH6+f D/A fs Digital-to-Analog Conversion Converter FLUFXLWWRWKHVLJQDO Transfer VSHFWUXPLVQHJOLJLEOH function A Analog Filter f A Analog output f fs SIGNAL OPERATION SPECTRUM Summary of spectral characteristics of a conventional D/A convertion system &<+(,('HSW+.3RO\8 24 Amplitude original Oversampling D/A system sample interpolated sample ■ time Several manufacturers have developed D/A After interpolation, higher bit-resolution is conversion methods which employ third- required to represent an interpolated value. order noise shaping. 1-bit 16-bit 24-bit 11-level 768X ■ Their design details differ somewhat, 1X 8X 32X 8x 3rd-order Digital D/A converter Analog oversampling Noise particularly in the noise shaping algorithms input (PWM+ LPF) output digital filter shaping and the low-bit output signal. ■ The MASH system codeveloped by NTT Block diagram of a MASH circuit and Matsushita is a multistage third-order noise shaping method. &<+(,('HSW+.3RO\8 25 &<+(,('HSW+.3RO\8 26 ■ One implementation of this design accepts ■ Digital-to-analog conversion is 16-bit words at a nominal sampling accomplished via PWM (pulse width frequency, and a digital filter stage performs modulation), outputting 1-bit data at a 768- 8-times oversampling and outputs 24-bit times oversampling rate. words. ■ Conversion is then performed by simply ■ Noise shaping circuits output data as an 11- passing the 1-bit stream through a low-pass value signal, at a 32-times oversampling filter. rate. &<+(,('HSW+.3RO\8 27 &<+(,('HSW+.3RO\8 28 2YHUDOO < ; ] 1 VWVWDJH VWRUGHU16FLUFXLW 8x O/S Noise PWM+ < ; ] 1 filter shaping LPF ■ Generally, if cascaded noise shaping 7ZRVWDJH FRQILJXUDWLRQ circuits exceed second order they can be LVXVHGWR prone to oscillation. DYRLG < < ] < ■ RVFLOODWLRQ MASH system avoids this through its QGVWDJH multistage configuration. QGRUGHU 16FLUFXLW < 1 ] 1 &<+(,('HSW+.3RO\8 29 &<+(,('HSW+.3RO\8 30 8x O/S Noise PWM+ filter shaping LPF ■ The outputs of each stage: ■ The final element in the system is D/A − conversion. Y = X + (1− z 1)N 1 1 ■ The eleven-value signal is converted into = − + − −1 2 Y2 N1 (1 z ) N2 pulses, each with a width corresponding to one value. ■ Resultant transfer function: ■ This can be accomplished by applying the = + − −1 = + − −1 3 Y Y1 (1 z )Y2 X (1 z ) N2 4-bit output of the DSP to a ROM to map 11 amplitude values into 22 time values with constant amplitude. &<+(,('HSW+.3RO\8 31 &<+(,('HSW+.3RO\8 32 %HFDXVHJUHDWWLPLQJDFFXUDF\FDQEHDFKLHYHG WKURXJKFU\VWDORVFLOODWRUVWKHZLGWKVDUHYHU\ DFFXUDWHDQGKHQFHWKHHUURURIWKHVLJQDOLVORZ ■ Because the signal is represented by a pulse width modulation waveform, conversion is performed by simply passing the signal through a low-pass filter. ■ Because great timing accuracy can be achieved through crystal oscillators, the widths are very accurate, and hence the error of the signal is low. &<+(,('HSW+.3RO\8 33 &<+(,('HSW+.3RO\8 34 A f Summary fs R x fs Digital input fs=Sampling Freq. k=No. of bits/sample A ■ R=Oversampling rate Such a method achieves 20-bit resolution, Transfer Digital function f A oversampling fs but greater resolution is possible. LPF f A R x fs Quantization f A noise added Noise R x fs shaper f A R x fs f D/A R x fs Converter Summary of spectral Transfer function characteristics A Analog of a LPF f A oversampling D/A convertion f f system with Analog output s SIGNAL noise shaping OPERATION SPECTRUM &<+(,('HSW+.3RO\8 35 &<+(,('HSW+.3RO\8 36 Revisit conventional system Analog input f =Sampling Freq. s Transfer A k=No. of bits/sample Application of Noise Shaping in function for Signal f A Analog LPF Analog-to-digital Conversion f Transfer A function for Quantization Signal noise added f A A A/D Converter f f A fs k bit fs f f s Digital output OPERATION SIGNAL SPECTRUM Summary of spectral characteristics of a conventional A/D convertion system &<+(,('HSW+.3RO\8 38 Oversampling A/D system Analog Sigma-delta Digital Decimation LPF Modulation LPF ■ An oversampling A/D converter is simple: ■ The input signal is first passed through a simple analog anti-aliasing filter, and the Analog domain Digital domain input signal is sampled at a very fast rate of Analog Digital R to extend the Nyquist frequency. input Analog Sigma-delta Digital output Decimation LPF Modulation LPF ■ The analog low-pass filter at the input is to remove the frequency components which 1-bit k-bit k-bit f =Rxf f =Rxf f s N s N N cannot be removed by the digital filter, but, because the preliminary sampling rate is Oversam pling A/D conversion high, the analog low-pass filter is low order. &<+(,('HSW+.3RO\8 39 &<+(,('HSW+.3RO\8 40 Analog Sigma-delta Digital Decimation LPF Modulation LPF ■ In any case, noise performance hinges on the oversampling rate and order of noise shaping employed. ■ The higher the order of the sigma-delta modulator we use, the lower the oversampling rate is required to achieve a given S/N performance. &<+(,('HSW+.3RO\8 41 &<+(,('HSW+.3RO\8 42 ,WFDXVHVOHVVKDUP HYHQWKRXJKDOLDVLQJ Analog Sigma-delta Digital Decimation LPF Modulation LPF GRHVRFFXU ■ The decimation process low-pass filters the ■ The decimation filter can be designed so signal and noise in the 1-bit code, that its frequencies of maximum attenuation bandlimiting the 1-bit code
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