Digital Audio Signal Processing, Second Edition

Chapter 3

AD/DA Conversions

The conversion of a continuous-time function x(t) (voltage, current) into a sequence of numbers x(n) is called analog-to-digital conversion (AD conversion). The reverse process is known as digital-to-analog conversion (DA conversion). The time-sampling of a function x(t) is described by Shannon's sampling theorem. This states that a continuous-time signal with bandwidth f_B can be sampled with a sampling rate f_S > 2f_B without changing the information content in the signal. The original analog signal is reconstructed by low-pass filtering with bandwidth f_B. Besides time-sampling, the nonlinear procedure of digitizing the continuous-valued amplitude (quantization) of the sampled signal occurs. In Section 3.1 basic concepts of Nyquist sampling, oversampling and delta-sigma modulation are presented. In Sections 3.2 and 3.3 principles of AD and DA converter circuits are discussed.

3.1 Methods

3.1.1 Nyquist Sampling

The sampling of a signal with sampling rate f_S > 2f_B is called Nyquist sampling. The schematic diagram in Fig. 3.1 shows the procedure. The band-limiting of the input at f_S/2 is carried out by an analog low-pass filter (Fig. 3.1a). The following sample-and-hold circuit samples the band-limited input at a sampling rate f_S. The constant amplitude of the time function over the sampling period T_S = 1/f_S is converted to a number sequence x(n) by a quantizer (Fig. 3.1b). This number sequence is fed to a digital signal processor (DSP) which performs signal ...