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Published byTracy Lee Modified over 9 years ago
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ADC AND DAC Sub-topics: Analog-to-Digital Converter -. Sampling
-. Quantizing -. Coding Digital-to-Analog Converter -. Teknik Sample and Hold. -. Teknik First-Order Hold -. Teknik Linear Interpolation with Delay
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Analog-to-Digital Converter
Most signals are analog e.g. speech, biological signals, seismic signals, radar signals, sonar signals, etc. ADC is applied to process analog signals by digital means ADC has a three-step process Sampling Quantization Coding Sampler Quantizer Coder A/D Converter Xa(t) X(n) Xq(n) 01011 … Analog Signal Discrete-Time Signal Quantized Digital Sinyal
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Sampling X(n) = xa(nT); -∞< n < ∞ t = nT = n/Fs
Fs = Sampling rate T = Sampling period
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Continuous-Time Signals Discrete-Time Signals
Relationship Among Frequency Variables Continuous-Time Signals Discrete-Time Signals Ω = 2F = 2f (radians/sec) Hz (radians/sample) (cycles/sample) = ΩT, f = F/Fs - Ω = /T, F = f ∙ Fs -½ f ½ -∞ < Ω < ∞ -π Ω π -∞ < F < ∞ -Fs/2 F Fs/2
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Sampling Theorem If the highest freq. contained in an analog signal xa(t) is Fmax = B and the signal is sampled at a rate Fs > 2 Fmax 2B, then xa(t) can be exactly recovered from its sample values using the interpolation function g(t) = (sin 2Bt)/(2Bt)
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Aliasing effect in sampling process
If x1(n) and x2(n) have the same output, i.e. sampling of high freq. analog signal is the same as sampling of low freq. analog signal
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Signal x(t) must a bandlimited signal
Therefore to solve the aliasing problem, sampling process should meet 2 requirements: Signal x(t) must a bandlimited signal The sampling rate fs must be min. 2fmax, i.e. fs 2 fmax or T 1/(2 fmax) Spectrum of Bandlimited Signal
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NYQUIST RATE Minimum sampling rate to avoid aliasing problem
fs = 2 fmax -> Nyquist rate fs/2 is Nyquist frequency or folding frequency or cutoff frequency [-fs/2, fs/2] = Nyquist Interval Antialiasing Prefilter
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Aplikasi fmax fs Sampling Rate of DSP Applications Geophysical 500 Hz
1 kHz Biomedical 2 kHz Mechanical 4 kHz Speech 8 kHz Audio 20 kHz 40 kHz Video 4 MHz 8 MHz
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Quantizing Quantization sample XQ(nT) that is B bits, has quantization levels 2B R = Range L=2B = quantization level Q = the width between quantization level
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The difference between the quantized value and the actual sample value
Quantization error: The difference between the quantized value and the actual sample value eq(n) = xq(n) – x(n) To eliminate the excess digits in quantization process, there are two techniques: Truncation Rounding: emax=Q/2
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Coding To assign a unique binary number to each quantization level
For L levels, at least L different binary numbers are required With a word length of b bits, 2b different binary numbers is created Therefore blog2L If word length is B+1 bit, therefore binary code combination is 2B+1, is equivalent to B+1log2L. Binary code is 012 … B with sequence as - … + b . 2-b 0 is the MSB (Most Significant Bit) and b is the LSB (Least Significant Bit)
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Digital-to-Analog Converter
Sample and Hold Technique First-Order Hold Technique Linear Interpolation with Delay Technique
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Sample and Hold Technique
Digital Input Signal Digital-to-analog converter Sample and Hold Lowpass smoothing filter Analog output
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First-order-Hold
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Linear Interpolation with Delay technique
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