Ling, Bingo WingKuen and Ho, Charlotte YukFan (2008) Can a second order bandpass sigma delta modulator achieve high signaltonoise ratio for lowpass inputs. Chaos, Solitons and Fractals, 37 (3). pp. 928930. ISSN 09760779
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letter_chao_SDM_second_order.pdf  Whole Document 60kB 
Full text URL: http://dx.doi.org/10.1016/j.chaos.2006.09.082
Abstract
Institutively, second order SDMs usually achieve lower SNR than high order ones because high order loop filters can achieve better noise shaping characteristics. Moreover, the signal transfer function should be designed to have large values and the noise transfer function should be designed to have small values at the passband of loop filters in order to achieve good noise shaping characteristics, so SNR should be high if input signal bands match passbands of loop filters and low otherwise. Based on this argument, one may expect that SNR will be low when input signals have lowpass characteristics while loop filters have bandpass characteristics.
However, since the above argument is based on the noise shaping theory which is formulated using a linear model, while quantizers in SDMs are nonlinear components, the linear model may not explain nonlinear system behaviors. In this letter, a counterexample is given to illustrate that a second order bandpass interpolative SDM may also give a very high SNR for lowpass inputs.
Item Type:  Article 

Additional Information:  Institutively, second order SDMs usually achieve lower SNR than high order ones because high order loop filters can achieve better noise shaping characteristics. Moreover, the signal transfer function should be designed to have large values and the noise transfer function should be designed to have small values at the passband of loop filters in order to achieve good noise shaping characteristics, so SNR should be high if input signal bands match passbands of loop filters and low otherwise. Based on this argument, one may expect that SNR will be low when input signals have lowpass characteristics while loop filters have bandpass characteristics. However, since the above argument is based on the noise shaping theory which is formulated using a linear model, while quantizers in SDMs are nonlinear components, the linear model may not explain nonlinear system behaviors. In this letter, a counterexample is given to illustrate that a second order bandpass interpolative SDM may also give a very high SNR for lowpass inputs. 
Keywords:  chaotic filter bank, cryptographical system, Cryptography using chaos 
Subjects:  H Engineering > H620 Electrical Engineering H Engineering > H310 Dynamics 
Divisions:  College of Science > School of Engineering 
ID Code:  2678 
Deposited By:  Bev Jones 
Deposited On:  13 Jun 2010 11:10 
Last Modified:  13 Mar 2013 08:39 
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