A statistical framework to minimise and predict the range values of quantisation errors in fixed-point FIR filters architectures

An analytic model for quantized discrete transform error

“…Although many different problems arising in connection with image [12,16,18,19,22,23], video [14] and speech [13] processing have need of quantization effect analysis, and although the very analysis has quite a rich history, being elaborated in earlier works such as [5,7] and then constantly advanced by research efforts such as [2,3,5,6,11,16,17,20,21,24,25], the special question of quantization under a linear transformation has apparently not yet been studied in depth.…”

“…The point is that every transform being used in practice, such as Fourier, DCT, Walsh, Haar, wavelet, or some, rather complicated by its formulation, overlapped transform type of MDCT (see, e.g., equations (1), (2) in [15], on page 554), from one mathematical point of view, is only a linear transformation that can always be simply written in the form…”

Statistical properties of quantisation noise in analogue‐to‐digital converter with oversampling and decimation

“…The present researches in this field related to LTI systems are focused on the improvements of the modelling procedures suitable for the fixed-point implementations [5][6][7][8][9] and for the floating-point [10] or the mixed-point implementations [11], and for the optimisation of the implementation parameters in order to obtain trade-off between the system realisation complexity and the output signal-to noise ratio that can be achieved [12][13][14][15].…”

“…Classical linear quantisation noise models provide estimated values of the mean, variance and the power spectrum of the quantisation noise at the output of the system [16]. In recent studies, the PDF of the output random signal is discussed as an important parameter [5, 9, 12, 15]. Typical initial assumption is that the PDF is Gaussian, because the output noise can be considered as a sum of independent random signals.…”