Chapter 2 Signal Sampling and Quantization 1 Sampling

Chapter 2 Signal Sampling and Quantization 1

Sampling of Continuous Signals • The ADC unit samples an analog signal, quantizes the sampled signal, and encodes the quantized signal level to a digital signal 2

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Sampling theorem: An analog signal can be in theory perfectly recovered as long as the sampling rate is at least twice larger than the highest frequency of the analog signal to be sampled Examples: • To sample a speech signal containing frequencies up to 4 k. Hz, the minimum sampling rate is chosen to be at least 8 k. Hz, or 8, 000 samples per second • For an audio signal with frequencies up to 20 k. Hz, sample the audio signal at the sampling rate of at least 40, 000 samples per second, or 40 k. Hz 4

• Sampling condition is satisfied. fmax=40 Hz, fs=100 Hz • Undersampling: Signal aliasing would occur when the sampling condition is not satisfied. fmax=90 Hz, fs=100 Hz 5

• View of sampling in frequency domain 6

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1. Sampling theorem establishes a minimum sampling rate for sampling a given band-limited analog signal with the highest frequency component of fmax If the sampling condition is satisfied, then the analog signal can be recovered via its sampled values 2. The half of the sampling frequency = Nyquist frequency (Nyquist limit) = folding frequency 8

Signal Reconstruction 9

• Anti-aliasing Lowpass Filter 10

Anti-aliasing filter (Butterworth type) 11

• Distortion due to the hold circuit and anti-image filter 12

ADC, DAC, and Quantization • ADC 13

• 3 -bit unipolar quantizer 14

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• 3 -bit bipolar quantizer 16

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• DAC 18

• Quantization error: • Quantization bound: • Signal to noise power ratio: 19

• Example 1: a 4 -bit bipolar quantizer 20

• Example 2: Speech, a 4 -bit bipolar quantizer 21