Alternative dual frames for digital-to-analog conversion in sigma–delta quantization

Alternative dual frames for digital-to-analog conversion in sigma-delta quantization

We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ , and λ > 1 is the oversampling ratio. We show that the counterpart...

Analog to Digital Conversion

1 ADC TYPES Analog-to-Digital Converters (ADCs) transform an analog voltage to a binary number (a series of 1’s and 0’s), and then eventually to a digital number (base 10) for reading on a meter, monitor, or chart. The number of binary digits (bits) that represents the digital number determines the ADC resolution. However, the digital number is only an approximation of the true value of the ana...

Photonic Analog-to-Digital Conversion

280 INTRODUCTION Accurate collection and processing of electromagnetic information is critical to a wide variety of applications. Present day RF and microwave sensor systems must cover many frequency bands, detect and identify a large range of signal powers, and analyze the signal information on an ever-decreasing time scale. Simultaneously achieving these attributes typically requires multiple...

Dithering in Analog-to-digital Conversion

Analog to digital conversion in physical measurements

There exist measuring devices where an analog input is converted into a digital output. Such converters can have a nonlinear internal dynamics. We show how measurements with such converting devices can be understood using concepts from symbolic dynamics. Our approach is based on a nonlinear one-to-one mapping between the analog input and the digital output of the device. We analyze the Bernoull...