NDLI: Quantization noise spectrum of double-loop sigma-delta converter with sinusoidal input

Content Provider	IEEE Xplore Digital Library
Author	Rangan, S. Leung, B.
Copyright Year	1993
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada (Rangan, S.; Leung, B.)
Abstract	An exact formula for the output noise spectrum of a double-loop sigma-delta modulator with a sinusoidal input is derived without the use of a white-noise model. In the case of a sinusoidal input with irrational input amplitude and digital frequency, the result agrees with the exact formula derived by ergodic theory for two-stage modulators. In addition, the present method also provides an exact formula for a sinusoidal input with rational frequency and amplitude. Furthermore, the period of the output with rational initial conditions and DC input is also calculated. All results assume that the quantizer does not overload, and hence apply only to multi-bit coders. The ergodic theory method for calculating the exact noise spectrum involves explicitly determining the autocorrelation of the internal quantization error with ergodic theory techniques, and then determining the noise spectrum from the correlation function. The present method, however, directly determines the quantization noise spectrum by using an open-loop model for the coder and applying a Fourier series representation of the quantization error function. The result of both of these methods is that the output noise spectrum for a sinusoidal input is composed of discrete spectral lines shaped by a sin/sup 4/(/spl omega2) envelope.<>
Starting Page	216
Ending Page	219
File Size	408455
Page Count	4
File Format	PDF
ISBN	0780317602
DOI	10.1109/MWSCAS.1993.343091
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1993-08-16
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quantization Delta-sigma modulation Frequency Signal to noise ratio Autocorrelation Fourier series Noise shaping Amplitude modulation Digital modulation Multi-stage noise shaping
Content Type	Text
Resource Type	Article

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