Lecture 2 Analog to digital conversion

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Lecture 2Analog to digital conversionBasic
discrete signals
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ADC process
DSP
Anti-aliasing filter
x(t)
ADC
x n

• Time discretization
• Amplitude discretization

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Time discretization
Shannon Sampling Theorem The sampling frequency
should be at least twice the maximum frequency
of the signal. fmax lt fs / 2 1/2T (fs/2
Nyquist frequency)

• Aliasing spurious low frequencies introduced by
  low sampling.
• The first stage in ADC is an anti-aliasing low
  pass filter!

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Amplitude discretization

• 1 bit ? 2 possible values
• 2 bits ? 4 possible values
• 8 bits ? 256 possible values
• 16 bits ? 65356 possible values
• N bits ? 2N possible values

Quantization noise
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• Dynamic range (max possible value min
  possible value)
• If too low
• Good resolution
• Risk of saturation
• If too high
• Poor resolution
• No saturation

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DAC process
DSP
Analog filter
x(t)
DAC
x n
Sample and hold
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Signal types
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Basic digital signals

• Why ?
• Complex signals can usually be expressed as
  summation of simple ones.
• For linear DSPs, if we know the response to
  basic signals we can predict the response to more
  complex ones.
• They can be used as test signals for studying
  properties of DSPs.

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Unit impulse function
d n
1

• n 0 n ? 0
• dn 1 n 0

n0 n
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Exponential function
x n
xn A an 0 lt a lt 1
n0 n
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Periodicity

• A signal is periodic if repeats after T values
• x n x nT x n2T
• T is the period of the signal
• Exercise Calculate the period of
• x n cos (?n/4)
• x n cos (3?n/4)

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Exercise

• Draw the following sequences
• x n un-2
• x n n un
• x n -3 dn4
• x n an a gt 1
• x n -2 u-n-2
• x n un2 un-6

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Exercise

• Find the mathematical expressions of the
  following sequences

a)
c)
b)
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Exercise

• Given the sequence of the figure, draw the
  following sequences
• a) xn-2
• b) x3-n
• c) xn-1 un
• d) xn-1 dn
• e) x1-n dn-2