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Digital Interfaces in Measurement Systems
Published in Robert B. Northrop, Introduction to Instrumentation and Measurements, 2018
Quoting Analog Devices’ AN-283 (sigma–delta ADCs and DACs): The final data rate reduction is performed by digitally resampling the filtered output using a process called decimation. The decimation of a discrete-time signal is shown in Fig. 6.12, where the sampling rate of the input signal x(n) is at a rate which is to be reduced by a factor of 4. The signal is resampled at the lower rate (the decimation rate), s(n) [fo]. Decimation can also be viewed as the method by which the redundant signal information introduced by the oversampling process is removed.In sigma-delta ADCs it is quite common to combine the decimation function with the digital filtering function. This results in an increase in computational efficiency if done correctly.
Conversion
Published in John Watkinson, The Art of Digital Audio, 2013
Oversampling means using a sampling rate which is greater (generally substantially greater) than the Nyquist rate. Neither sampling theory nor quantizing theory require oversampling to be used to obtain a given signal quality, but Nyquist rate conversion places extremely high demands on component accuracy when a convertor is implemented. Oversampling allows a given signal quality to be reached without requiring very close tolerance, and therefore expensive, components. Although it can be used alone, the advantages of oversampling are better realized when it is used in conjunction with noise shaping. Thus in practice the two processes are generally used together and the terms are often seen used in the loose sense as if they were synonymous. For a detailed and quantitative analysis of oversampling having exhaustive references the serious reader is referred to Hauser.28
Digital audio signals
Published in John Watkinson, The Art of Sound Reproduction, 2012
Oversampling means using a sampling rate which is greater (generally substantially greater) than the Nyquist rate. Neither sampling theory nor quantizing theory require oversampling to be used to obtain a given signal quality, but Nyquist rate conversion places extremely high demands on component accuracy when a converter is implemented. Oversampling allows a given signal quality to be reached without requiring very close tolerance, and therefore expensive, components. Although it can be used alone, the advantages of oversampling are better realized when it is used in conjunction with noise shaping. Thus in practice the two processes are generally used together and the terms are often seen used in the loose sense as if they were synonymous. For a detailed and quantitative analysis of oversampling having exhaustive references the serious reader is referred to Hauser.18
Exponential approximation of multivariate bandlimited functions from average oversampling
Published in Applicable Analysis, 2022
We are concerned with the case when only finitely many sample data are available. Set for . Looking at the Shannon series in (1), let us assume that we have the finite sample data of some . Naturally, one tends to truncate the Shannon series (1) as a manner of approximately reconstructing f. This turns out to be the optimal reconstruction method in the worst case scenario [10,11]. However, this method is of the slow approximation rate of , [12–15]. Dramatic improvement of the approximation rate can be achieved by using oversampling data. Here, oversampling means to sample at a rate strictly less than the Nyquist sampling rate . Through a change of variables if necessary, we assume that the bandwidth and functions in are sampled at the integer points, thus constituting oversampling as .
A Low-distortion Hardware Efficient MASH
Published in Smart Science, 2018
Rijo Sebastian, Babita Roslind Jose, T. K. Shahana, Jimson Mathew
The demand for high-performance and low power electronic systems often required in next generation wideband applications has intensified the research attention toward developing new efficient wideband analog to digital converter (ADC) architectures. ADC act as a key element in many communication systems. Compared to other kind of ADCs, sigma delta ADC ( ADC) is well suited for medium to high resolution wideband applications. ADC achieves high resolution through oversampling and noise shaping techniques [1]. The ADCs used in higher bandwidth applications are often designed at low oversampling ratio (OSR) due to CMOS technology scaling constraints. A low value of OSR will obviously decrease the achievable signal to noise ratio (SNR). The techniques to improve the resolution in the case of low OSR include increasing the order of loop filter and employing a multi-bit quantizer. The cascaded or multi-stage noise shaping (MASH) modulator architecture eliminates the loop filter instability problems associated with the single-loop higher order modulator structures and became appropriate for the broadband applications. In MASH architecture, the quantization noise of the first-stage modulator is extracted and provided to the next stage as input. An appropriate digital signal processing logic cancels the quantization noise of all except the last stage. The last stage quantization noise is shaped by a noise transfer function (NTF) of order equal to the sum of all the orders.