Chapter 3 Sampling

Zero-order hold interpolation Nearest neighbor interpolation (3-14) Fig. 3-9.

In frequency domain Induces distortion in the reconstructed signal Resolution error inside Nyquist frequency Aliasing error beyond Nyquist frequency Ideal low-pass filter Zero-order hold interpolation function Fig. 3-10.

Applying low-pass filtering for smoothing Smoothing filter Fig. 3-11.

First-order hold interpolation Linear interpolation (3-15) Fig. 3-12.

Comparison of interpolation functions Ideal interpolation function Zero-order hold interpolation function First-order hold interpolation function Fig. 3-13.

Analog to Digital Conversion Digital signal processing Anti-aliasing filter (pre-filter) To reduce aliasing and to limit within Nyquist frequency A/D converter Converting the analog input signal into digital form D/A converter Converting processed digital signal back into analog form Smoothing filter Smoothing the reconstructed signal and removing unwanted high frequency components Anti-aliasing filter (LPF) A/D converter Digital processors D/A Smoothing filter Fig. 3-14.

Analog to digital conversion process Sampling Converting analog signal into discrete-time signal Quantizer Each discrete-time signal sample is quantized into one of levels Encoder Encoding the discrete levels into distinct binary word, each of length B bits Lowpass filter Sample and hold Quantizer Encoder Fig. 3-15.

Quantization Quantization error (3-16) x(t) and Quantization Fig. 3-16.

Max. quantization error If q is least-significant bit(LSB) Quantization error using probability density function Average and variance (3-17) Fig. 3-17.

Quantization interval Variance of quantization error Signal-to-noise ratio (3-18) (3-19) (3-20)

Example 3-1 Mean-square quantization error(MSQE)