Weighted Median Filters with Sigma-Delta Modulation Encoding

Oversampled sigma-delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon. Digital decimation filters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we first s

Weighted Median Filters with Sigma-Delta Modulation Encoding 1Department of Electrical and Computer Engineering University of Delaware Newark, Delaware 19716 (302) 831-8030 arce@ee.udel.eduAbstractOversampled sigma-delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon. Digital decimation lters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we rst show that weighted median ltering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Through a simple modi cation of the binary time-series outputted by the A/D modulator, the sequence obtained after the SDM demodulator is shown to be equivalent to weighted median ltering the multilevel sequence at the Nyquist rate. Secondly, we show that weighted median (WM) lters can be used for SDM decimation lters and that these lters are readily implemented in the SDM binary domain. A very promising characteristic of SDM converters equipped with weighted median decimating lters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals can be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. The proposed signal processing algorithms, in essence, combine A/D sigma-delta converters and weighted median lters into a single programmable system. Finally, a joint WM lter and SDM A/D tunable converter equipped with WM decimating lters is presented.Submitted to the IEEE Transactions on Signal Processing

G. R. Arce, N. Grabowski, and N. C. Gallagher

SP Paper Category 2.1.5 (Rank order and median lters)1 This work was supported in part by the National Science Foundation through the Microelectronic Information Processing Systems Division under the grant MIP-9530923.

Oversampled sigma-delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon. Digital decimation filters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we first s

1 IntroductionOversampled sigma-delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon 1]. Among the reasons of the increasing popularity of SDM are: (a) high resolution quantization is attained with simple circuits, (b) these are robust to circuit imperfections, (c) allows for speed vs. resolution tradeo s, and (d) lower cost of implementations. Sigma-delta modulation extends the concept of delta modulation by preemphasizing the low frequencies of the input by the use of an integrator. As a result, slope-overload and granular noise distortions, typical of delta modulation, are reduced. In addition, the de-emphasis (differentiator) required at the decoder, to account for the pre-emphasis placed at the input signal, cancels the integrator in the DM decoder, resulting in a much simpli ed decoder consisting of a low pass digital lter. To describe the principles of SDM A/D converters, it is useful to cast them within the framework of conventional uniform quantizers 2. A b-bit uniform quantizer Q x(n)] maps a real-valued input signal x(n)

into one of 2b quantization values. Let the range of the X quantizer be X, then the quantizer step size is where= 2 . The quantizer error is e(n)= x(n)? Q x(n)] with?=2< e(n)=2 for x(n) 2 dynamic range. A simpli ed model assumes e(n) is an additive white noise term xq (n)= Q x(n)]= x(n)+ e(n) with 2 e(n) U (?=2;=2). The quantization noise power is e= 122 . The signal to noise 2 ratio can be shown to be SNR= 10 log10 2= 6:02b+ 10:8? 20 log10 X2 . Thus, the SNR increases approximately by 6 dB for each bit added to the quantization wordlength code. When the analog input signal is sampled at 2RB (oversampled by R) and a uniform quantizer of b bits is applied, the power spectrum of x(n) is depicted in Fig. 1(a). The quantization error embedded in the power spectrum Se(f ) is now spread over a larger region but the signal power contained in Sx(f ) is still concentrated within itsb x e x

2

In-depth reviews of SDM converters can be found in 1, 2].

Oversampled sigma-delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon. Digital decimation filters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we first s

1 bandwidth. The height of the quantization error spectra is ER= 2B R . The in2 2 band noise power is n= 2BER= R; and the SNR can be computed as SNR= 2 2 10 log10 2= 10 log10(R)+ 10 log10 2 . For PCM, doubling the sampling frequency decreases the in-band noise by 3 dB increasing the resolution by half a bit.e

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f-2RB -B 0 B 2RB

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Figure 1: Power spectrum of (a) oversampled PCM signal, (b) oversampled SDM signal Sigma delta A/D converters use oversampling in a more e cient way. The simplest SDM encoder is the so called single-loop sigma delta modulator whose discrete time circuit model is shown in Fig. 2. The circuit consists of a one-bit quantizer inside a feedback loop and is operated at a higher rate than the Nyquist frequency (oversampling). Let fs and fN be the sampling frequency and the Nyquist frequency, respectively; the oversampling ratio is de ned as R= fs=fN . Let xc(t) and x(n)= xc (nTR ) be the input analog signal and the oversampled discrete-time se …… 此处隐藏：22604字，全部文档内容请下载后查看。喜欢就下载吧 ……