3. Digital Implementation of Mo/Demodulators

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3. Digital Implementation of Mo/Demodulators
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General Structure of a Mo/Demodulator
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Single Side Band (SSB) Modulator
MOD
SSB
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Implementation using Real Components
SSB
where
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Single Side Band (SSB) Demodulator
DEM
LPF
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Single Side Band (SSB) Modulator in Discrete Time
Modulator Implemented in two stages
Digital Up Converter
DUC
Analog MOD
ZOH
DISCRETE TIME
CONTINUOUS TIME
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Single Side Band (SSB) Demodulator in Discrete
Time
Demodulator Implemented in two stages
Digital Down Converter
DDC
Analog DEM
ZOH
DISCRETE TIME
CONTINUOUS TIME
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Digital Down (DDC) and UP (DUC) Converters
DUC
DDC
RF
Baseband

• MHz for voice
• GHz for data

• kHz for voice
• MHz for data

Order of magnitude of resampling
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Problem with Large Upsampling Factor
if M is large, very small transition region
high complexity filter
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Problem with Large Downsampling Factor
LPF
LPF
if M is large, very small transition region
high complexity filter
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Solution Upsample in Stages
In order to make it more efficient we upsample in
L stages
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i-th Stage of Upsampling
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Example Upsample in One Stage
This is not only a filter with high complexity,
but also it is computed at a high sampling rate.
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Same Example in Three Stages
Total Number of operations/sec
a 95 savings!!!!
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Downsample in Stages
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i-th Stage of Downsampling
noise
keep aliased noise away from signal
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Example Downsample in One Stage
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Same Example in Three Stages
Total Number of operations/sec
a savings of almost 99 !!!
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Stages at the Highest Rates
highest rates

• the highest sampling rates are close to carrier
  frequencies, thus very high
• properly choose intermediate frequencies to have
  simple filters at highest rates

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Last Stage in UpSampling
wide region
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First Stage in DownSampling
wide region
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Very simple Low Pass Filter the Comb Integrator
Cascade (CIC)
same!!!
Comb
Integrator
these two are the same!
Notice no multiplications!
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Frequency Response of the Comb Filter
like a comb!
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Impulse Response of the CIC
interpolating sequence
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The CIC in the Time Domain
like a discrete time ZOH!
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Two Important Identities The Noble Identities
Same !!!
As a consequence we have one of two Noble
Identities
Same!!!
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Other Noble Identity
Same !!!
As a consequence we have the other of the two
Noble Identities
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Efficient Implementation of Upsampling CIC
Use Noble Identity
Very simple implementation (no multiplications)
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Efficient Implementation of Downsampling CIC
Use Noble Identity
Very simple implementation (no multiplications)
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Frequency Response of the CIC
Not a very good Low Pass Filter. We want a better
attenuation in the stopband!
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Put M Stages together
Frequency Response
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Improved Frequency Response of CIC Filter
Resampling Factor N10
With M4 or 5 we already get a very good
attenuation.
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Example M4 Stages
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Implementation of M Stage CIC Filter Upsampling
Use Noble Identity
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Implementation of M Stage CIC Filter Downsampling
Use Noble Identity
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Problem DownSampling CIC is Unstable
Now we have to be careful the output of the
integrator will easily go to infinity
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CIC Implementation.
At the p stage
This implies
and
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If we use Q bits for the integrators then we
need to guarantee
Let the input data use L bits
Then
decimation factor
input bits
number of stages
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Application Software Defined Radio

• Definitions
• Software Defined Radio modulation, bandwidth
  allocation all in software
• Field Programmable Gate Array (FPGA)
  reprogrammable logic device which is able to
  perform a number of operations in parallel. They
  can process data at a rate of several 100s of MHz
• DSP Chip optimized for DSP operations by some
  hardwired ops (such as multiplies).

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An HF SSB Software Defined Radio by Dick Benson,
The Mathworks,
64MHz
15.6kHz
7.8kHz
RF
IQ
AUDIO
Rec.
Rec.
Rec/Tr
Trans.
Trans.
DAC
IQ
AUDIO
RF
FPGA
DSP Chip
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Transmitter
AUDIO
I
FIR
SSB
Q
FIR
DSP Chip
Xilinx Library Modules
I
FIR
FIR
CIC
RF
Q
FIR
FIR
CIC
FPGA
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Receiver
Xilinx Library Modules
I
RF
CIC
FIR
FIR
Q
CIC
FIR
FIR
FPGA
I
FIR
AUDIO
Q
FIR
DSP Chip