Transcript ADC, DAC, AND DISCRETE

PSD, ADC & DAC
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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PSD, ADC & DAC
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
A/D
Converter
Xa(t)
Sampler
Analog Signal
X(n)
Discrete-Time
Signal
Quantizer
Xq(n)
Quantized
Signal
Coder
01011
…
Digital Sinyal
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PSD, ADC & DAC
• Sampling
• X(n) = xa(nT); -∞< n < ∞
• t = nT = n/Fs
– Fs = Sampling rate
– T = Sampling period
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PSD, ADC & DAC
Relationship Among Frequency Variables
Continuous-Time
Signals
Discrete-Time Signals
Ω = 2F
 = 2f
(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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PSD, ADC & DAC
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 2Bt)/(2Bt)
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PSD, ADC & DAC
• 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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PSD, ADC & DAC
• 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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PSD, ADC & DAC
• 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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PSD, ADC & DAC
Sampling Rate of DSP Applications
Aplikasi
fmax
fs
Geophysical
500 Hz
1 kHz
Biomedical
1 kHz
2 kHz
Mechanical
2 kHz
4 kHz
Speech
4 kHz
8 kHz
Audio
20 kHz
40 kHz
Video
4 MHz
8 MHz
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PSD, ADC & DAC
• Quantizing
• Quantization sample XQ(nT) that is B bits, has
quantization levels 2B
Q
R
2B
R
L   2B
Q
– R = Range
– L=2B = quantization level
– Q = the width between quantization level
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PSD, ADC & DAC
• 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
Q
Q
 e
2
2
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PSD, ADC & DAC
• 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 blog2L
– If word length is B+1 bit, therefore binary code
combination is 2B+1, is equivalent to B+1log2L.
– Binary code is 012 … B with sequence as
-0 . 20 + 1 . 2-1 + 2 . 2-2 + … + b . 2-b
– 0 is the MSB (Most Significant Bit) and b is the LSB
(Least Significant Bit)
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PSD, ADC & DAC
Digital-to-Analog Converter
 Sample and Hold Technique
 First-Order Hold Technique
 Linear Interpolation with Delay Technique
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PSD, ADC & DAC
• Sample and Hold Technique
Digital
Input
Signal
Digitalto-analog
converter
Sample
and
Hold
Lowpass
smoothing
filter
Analog
output
Signal
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• First-order-Hold
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• Linear Interpolation with Delay technique
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