Data ConversionImage HalftoningSlide 3Digital Halftoning MethodsScreening (Masking) MethodsGrayscale Error DiffusionOld-Style A/D and D/A ConvertersCost of Multibit Conversion Part I: Brickwall Analog FiltersCost of Multibit Conversion Part II: Low- Level LinearitySolutionsSolution 1: OversamplingSolution 2: Add DitherTime Domain Effect of DitherFrequency Domain Effect of DitherSolution 3: Noise ShapingPutting It All TogetherEE445S Real-Time Digital Signal Processing Lab Fall 2014Lecture 10Data ConversionSlides by Prof. Brian L. Evans, Dept. of ECE, UT Austin, and Dr. Thomas D. Kite, Audio Precision, Beaverton, OR [email protected] Dr. Ming Ding, when he was at the Dept. of ECE, UT Austin, converted slides by Dr. Kite to PowerPoint formatSome figures are from Ken C. Pohlmann, Principles of Digital Audio, McGraw-Hill, 1995.10 - 2Image Halftoning•Handout J on noise-shaped feedback codingDifferent ways to perform one-bit quantization (halftoning)Original image has 8 bits per pixel original image (pixel values range from 0 to 255 inclusive)•Pixel thresholding: Same threshold at each pixelGray levels from 128-255 become 1 (white)Gray levels from 0-127 become 0 (black) •Ordered dither: Periodic space-varying thresholdingEquivalent to adding spatially-varying dither (noise)at input to threshold operation (quantizer)Example uses 16 different thresholds in a 4  4 maskPeriodic artifacts appear as if screen has been overlaid No noise shapingNo noise shaping10 - 3Image Halftoning•Error diffusion: Noise-shaping feedback codingContains sharpened original plus high-frequency noiseHuman visual system less sensitive to high-frequency noise (as is the auditory system)Example uses four-tap Floyd-Steinberg noise-shaping(i.e. a four-tap IIR filter)•Image quality of halftonesThresholding (low): error spread equally over all freq.Ordered dither (medium): resampling causes aliasingError diffusion (high): error placed into higher frequencies•Noise-shaped feedback coding is a key principle in modern A/D and D/A converters10 - 4Digital Halftoning MethodsClustered Dot ScreeningAM HalftoningBlue-noise MaskFM Halftoning 1993Dispersed Dot ScreeningFM HalftoningGreen-noise HalftoningAM-FM Halftoning 1992Error DiffusionFM Halftoning 1975Direct Binary SearchFM Halftoning 199210 - 5Screening (Masking) Methods•Periodic array of thresholds smaller than imageSpatial resampling leads to aliasing (gridding effect)Clustered dot screening produces a coarse image that is more resistant to printer defects such as ink spreadDispersed dot screening has higher spatial resolution256*3231,3229,3227,3225,3223,3221,3219,3217,3215,3213,3211,329,327,325,323,321Thresholds10 - 6Error DiffusionHalftoneGrayscale Error Diffusion•Shapes quantization error (noise)into high frequencies•Type of sigma-delta modulation•Error filter h(m) is lowpasscurrent pixelweights3/167/165/16 1/16b(m)+__+e(m)x(m)difference thresholdcompute error (noise)shapeerror (noise)u(m))(mhFloyd-Steinberg filter h(m)Spectrum10 - 7Old-Style A/D and D/A Converters•Used discrete components (before mid-1980s)•A/D ConverterLowpass filter hasstopband frequencyof ½ fs•D/A ConverterLowpass filter hasstopband frequencyof ½ fsDiscrete-to-continuousconversion could be assimple as sample and holdAnalog Lowpass FilterQuantizerSampler at sampling rate of fsAnalog Lowpass FilterDiscrete to Continuous Conversionfs10 - 8ABCDPohlmann Fig. 3-5 Two examples of passive Chebyshev lowpass filters and their frequency responses. A. A passive low-order filter schematic. B. Low-order filter frequency response. C. Attenuation to -90 dB is obtained by adding sections toincrease the filter’s order. D. Steepness of slope and depth of attenuation are improved.Cost of Multibit Conversion Part I:Brickwall Analog Filters10 - 9Pohlmann Fig. 4-3 An example of a low-level linearity measurement of a D/A converter showing increasing non-linearity with decreasing amplitude.Cost of Multibit Conversion Part II:Low- Level Linearity10 - 10Solutions•Oversampling eases analog filter designAlso creates spectrum to put noise at inaudible frequencies•Add dither (noise) at quantizer inputBreaks up harmonics (idle tones) caused by quantization•Shape quantization noise into high frequenciesAuditory system is less sensitive at higher frequencies•State-of-the-art in 20-bit/24-bit audio convertersOversampling 64x 256x 512xQuantization 8 bits 6 bits 5 bitsAdditive dither 2-bit  PDF 2-bit  PDF 2-bit  PDFNoise shaping 5th / 7th order 5th / 7th order 5th / 7th orderDynamic range 110 dB120 dB120 dB10 - 11A. A brick-wall filter must sharply bandlimit the output spectra. B. With four-times oversampling, images appear only at the oversampling frequency.C. The output sample/hold (S/H) circuit can be used to further suppress the oversampling spectra.Solution 1: OversamplingPohlmann Fig. 4-15 Image spectra of nonoversampled and oversampled reconstruction.Four times oversampling simplifies reconstruction filter.10 - 12Pohlmann Fig. 2-8 Adding dither at quantizer input alleviates effects of quantization error. A. An undithered input signal with amplitude on the order of one LSB.B. Quantization results in a coarse coding over two levels. C. Dithered input signal.D. Quantization yields a PWM waveform that codes information below the LSB.Solution 2: Add Dither10 - 13A A 1 kHz sinewave with amplitude of one-half LSB without dither produces a square wave. C Modulation carries the encoded sinewave information, as can be seen after 32 averagings.B Dither of one-third LSB rms amplitude is added to the sinewave before quantization, resulting in a PWM waveform.D Modulation carries the encoded sinewave information, as can be seen after 960 averagings.Pohlmann Fig. 2-9 Dither permits encoding of information below the least significant bit. Vanderkooy and Lipshitz.Time Domain Effect of Dither10 - 14unditheredditheredundithered ditheredPohlmann Fig. 2-10 Computer-simulated quantization of a low-level 1- kHz sinewave without, and with dither. A. Input signal. B. Output signal (no dither). C. Total error signal (no dither). D. Power spectrum of output signal (no dither). E. Input signal. F. Output signal (triangualr pdf dither). G. Total error signal (triangular pdf dither). H. Power spectrum of output signal (triangular pdf dither) Lipshitz, Wannamaker, and VanderkooyFrequency Domain Effect of Dither10 - 15We have a two-bit DAC and four-bit input signal words.