Lecture 2 (ADC & DAC).pptx - Digital Signal Processing 1 Lecture-2 Signal Sampling and Quantization Agenda 2 Sampling of Continuous Signal Signal

Lecture 2 (ADC & DAC).pptx - Digital Signal Processing...

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Digital Signal Processing Lecture-2 Signal Sampling and Quantization 1
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Agenda 2 Sampling of Continuous Signal Signal Reconstruction Analog-to-Digital Conversion, Digital-to- Analog Conversion, and Quantization Summary Li Tan and Jean Jiang, “DSP Fundamentals and Applications”, 2 nd Edition, 2013, Elsevier.
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Sampling of Continuous Signal 3
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Sampling of Continuous Signal 4 Figure 1: A digital signal processing scheme. Figure 1 describes a simplified block diagram of a digital signal processing (DSP) system. Li Tan and Jean Jiang, “DSP Fundamentals and Applications”, 2 nd Edition, 2013, Elsevier.
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Just what does an A/D converter DO? Converts analog signals into binary words
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Concept of Sampling 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 levels to the digital signal.
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A simple ADC
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Why Sampling? Impossible to digitize an infinite number of points because it requires infinite amount of memory and infinite amount of processing power for computations. Sampling can solve such a problem by taking samples at the fixed time interval, as shown in figures, where the time T represents the sampling interval or sampling period in seconds. This process is called sample and hold . Since there exists one amplitude level for each sampling interval.
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Sampling Rate For a given sampling interval T, which is defined as the time span between two sample points, the sampling rate is therefore given by: For example, if a sampling period is T =125 µs, the sampling rate is determined as fs =1/125 µs = 8,000 samples per second (Hz). T f s 1
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Sampling Rate After the analog signal is sampled, we obtain the sampled signal whose amplitude values are taken at the sampling instants, thus the processor is able to handle the sample points . Next, we have to ensure that samples are collected at a rate high enough that the original analog signal can be reconstructed or recovered later . In other words, we are looking for a minimum sampling rate to acquire a complete reconstruction of the analog signal from its sampled version .
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Aliasing If an analog signal is not appropriately sampled, aliasing will occur, which causes unwanted signals in the desired frequency band. The sampling theorem guarantees that an analog signal can be in theory perfectly recovered as long as the sampling rate is at least twice as large as the highest-frequency component of the analog signal to be sampled . The condition is described as: max 2 f f s
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Sampling Theorem Concept (Cont…) Here, f max is the maximum-frequency component of the analog signal to be sampled.
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