Approximating a Bandlimited Function Using Very Coarsely Quantized Data: Improved Error Estimates in Sigma-delta Modulation
نویسنده
چکیده
This paper concerns fine analytical error estimates in analog-to-digital conversion of bandlimited functions using the method of sigma-delta modulation (also called Σ∆ quantization). This method has found widespread usage in practice due to several advantages in its implementation compared to conventional methods (see [1, 11]). A recent mathematical treatment of this problem appears in [3]. Below we give a quick introduction as well as setting our notation. We define the class BΩ of Ω-bandlimited functions to be the space of real-valued continuous functions in L∞(R) whose Fourier transforms (as distributions) have supports contained in [−Ω,Ω]. We denote the Fourier transform of x by x̂, which is defined by x̂(ξ) = ∫ ∞
منابع مشابه
Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order
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