Explain the quantization effects in design of digital filters
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Digital filters are widely used in modern signal-transmission systems. The first-order filters are used for extracting lower-frequency or upper-frequency signals. Quantization errors due to the finite number of binary digits in the representation of numbers are typical of digital filters.
Quantization is a representation of data samples with a certain number of bits per sample after rounding to a suitable level of precision. Quantization errors in a Digital Signal Processing (DSP) system can be introduced from three sources; one source is input quantization, a second is coefficient quantization and the third is the finite precision in the arithmetic operations.
The quantization error in the arithmetic operations can be controlled by carefully selecting the size of buffer registers according to the input word length. Quantization errors from input and filter samples are considered in this article. The effects of quantization errors and the tradeoffs required between precision and hardware resources are discussed in relation to the implementation of the DSP in Field Programmable Gate Array (FPGA).
This article is divided into three main sections; quantization effects for upconversion, quantization noise due to rounding off arithmetic and quantization effects for digital beamforming (DBF). Fixed length samples cause reduction in the filter dynamic range and gain resolution.
Quantization is a representation of data samples with a certain number of bits per sample after rounding to a suitable level of precision. Quantization errors in a Digital Signal Processing (DSP) system can be introduced from three sources; one source is input quantization, a second is coefficient quantization and the third is the finite precision in the arithmetic operations.
The quantization error in the arithmetic operations can be controlled by carefully selecting the size of buffer registers according to the input word length. Quantization errors from input and filter samples are considered in this article. The effects of quantization errors and the tradeoffs required between precision and hardware resources are discussed in relation to the implementation of the DSP in Field Programmable Gate Array (FPGA).
This article is divided into three main sections; quantization effects for upconversion, quantization noise due to rounding off arithmetic and quantization effects for digital beamforming (DBF). Fixed length samples cause reduction in the filter dynamic range and gain resolution.
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Quantization effects in digital filters can be divided into four main categories: quantization of system coefficients, errors due to A-D conversion, errors due to roundoffs in the arithmetic, and a constraint on signal level due to the requirement that overflow must be prevented in the comparison. The effects of quantization on implementations of two basic algorithms of digital filtering-the first-or second-order linear recursive difference equation, and the fast Fourier transform (FFT) - are studied in some detail. For these algorithms, the differing quantization effects of fixed point, floating point, and block floating point arithmetic are examined and compared. The ideas developed in the study of simple recursive filters and the FFT are applied to analyze the effects of coefficient quantization, roundoff noise, and the overflow constraint in two more complicated types of digital filters - frequency sampling and FFT filters. Realizations of the same filter design, by means of the frequency sampling and FFT methods, are compared on the basis of differing quantization effects. All the noise analyses in the report are based on simple statistical models for roundoff and A-D conversion errors. Experimental noise measurements testing the predictions of these models are reported, and the empirical results are generally in good agreement with the statistical predictions.
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