Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 15

CHAPTER

2

Signal Sampling and Quantization

CHAPTER OUTLINE

2.1 Sampling of Continuous Signal........................................................................................................ 15
2.2 Signal Reconstruction .................................................................................................................... 21
2.2.1 Practical Considerations for Signal Sampling: Anti-Aliasing Filtering................................25
2.2.2 Practical Considerations for Signal Reconstruction: Anti-Image Filter and Equalizer ..........30
2.3 Analog-to-Digital Conversion, Digital-to-Analog Conversion, and Quantization .................................... 35
2.4 Summary ....................................................................................................................................... 47
2.5 MATLAB Programs .......................................................................................................................... 48

OBJECTIVES:
This chapter investigates the sampling process, sampling theory, and the signal reconstruction
process. It also includes practical considerations for anti-aliasing and anti-image filters and signal
quantization.

2.1 SAMPLING OF CONTINUOUS SIGNAL
As discussed in Chapter 1, Figure 2.1 describes a simplified block diagram of a digital signal
processing (DSP) system. The analog filter processes the analog input to obtain the band-limited
signal, which is sent to the analog-to-digital conversion (ADC) unit. The ADC unit samples the
analog signal, quantizes the sampled signal, and encodes the quantized signal level to the digital
signal.
Here we first develop concepts of sampling processing in the time domain. Figure 2.2 shows an
analog (continuous-time) signal (solid line) defined at every point over the time axis (horizontal line)
and amplitude axis (vertical line). Hence, the analog signal contains an infinite number of points.
It is impossible to digitize an infinite number of points. The infinite points cannot be processed by
the digital signal (DS) processor or computer, since they require an infinite amount of memory and
infinite amount of processing power for computations. Sampling can solve such a problem by taking
samples at a fixed time interval as shown in Figure 2.2 and Figure 2.3 , where the time T represents the
sampling interval or sampling period in seconds.
As shown in Figure 2.3 , each sample maintains its voltage level during the sampling interval T to
give the ADC enough time to convert it. This process is called sample and hold . Since there exits one
amplitude level for each sampling interval, we can sketch each sample amplitude level at its corre-
sponding sampling time instant shown in Figure 2.2 , where 14 samples at their sampling time instants
are plotted, each using a vertical bar with a solid circle at its top.