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7/30/2019 DSP Lecture 18
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Lectures 18 EE-802 ADSP SEECS-NUST
EE 802-Advanced Digital SignalProcessing
Dr. Amir A. Khan
Office : A-218, SEECS
9085-2162; [email protected]
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Lectures 18 EE-802 ADSP SEECS-NUST
Lecture Outline
Sampling of Bandpass signals(taken from Understanding DSP by Lyons)
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Lectures 18 EE-802 ADSP SEECS-NUST
Bandpass Signals vs Low-pass Signals
Bandpass signal : Centered at some frequency other than
origin (recall modulated signals)
Nyquist criteria for bandlimited (low-pass signals) requires
sampling at least at twice the highest frequency
Highest frequency may be too high for bandpass signals Bandpass sampling thus samples at a lower rate, dependent
more so on the bandwidth than the highest frequency
What do we buy with a lower sampling rate?
Reduced speed requirement on A/D converters
Reduction of memory requirement for sample storage
You just cannot sample band pass signals at any arbitrary high
rate of your own liking3
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Bandpass signal
centered atfc=20 MHzbandwidth ofB=5 MHz
Nyquist Sampling Rate
45 MHz (2 x 22.5 MHz)
Consider sampling atsub-Nyquist rate
(e.g.fs =17.5 MHz)
Replicas of original spectrum
appear every 17.5 MHz from
original location
Is this sampling OK ?
Indeed as we have no aliasing and can thus recover our original signal
Inherent frequency translation associated with sampling is playing to our advantage
OK, can we sample at a still lower rate ?
Yes, but how low?
Bandpass Sampling-See for yourself
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General Condition for Sampling Rate
(Bandpass signals)
Consider a bandpass signal spectrum
Choosefs so that two side bands align
together at origin without overlapping
fs = fc B/2
What should befs to fitm SSBs*
in thespace2fcB?
fs =fcB/2 resulted in 2 SSBs*
mfs = (2fc B) willresult in m replicas
?
m = 6
m
Bff cs
2
SSB* : single side band also called replica 5
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General Condition for Sampling Rate
(Bandpass signals)
m
Bff cs
2What is the influence of increasing
fs beyond above range?
P band shifts right from origin
Q band shifts left from origin
Aliasing will occur
Choice of m
As long asfsis not less than 2B
What is the influence of reducing
fs tofs below above range?
P band (and associated replicas)
shift left Q band (and associated replicas)
shift right
Till we have the situation where P overlaps with original spectrum
1
2''
m
Bff cs
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Conditions for Bandpass Sampling-Example
m Bffm Bfc
sc
2
1
2
wheremis an integer so that Bfs 2
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Example : m = 1
m
Bf
fm
Bf cs
c
2
1
2
Baseband available in this case 8
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Example : m = 2
m
Bf
fm
Bf cs
c
2
1
2
Baseband available in this case
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Example : m = 3 and m = 5
m
Bf
fm
Bf cs
c
2
1
2
Baseband available in this case
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Summary of Example and Possible Choices
Optimum sampling rate to be chosen according to the availability of baseband
in the sampled spectrum
So which one to choose b/w the 3 optimum sampling rates possible? Depends on the actual application and hardware availability
Digital telephony for example requires sampling rates in multiples of 8 KHz
Certain hardware may perform better at higher frequencies
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Graphical View Bandpass Sampling
m
Bf
fm
Bf cs
c
2
1
2
Normalized sampling rates as
function ofR allow quick selectionof sampling frequencies
Shaded regions represent forbidden
zones where sampling frequency
cannot be chosen
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Graphical View -Example
m
Bf
fm
Bf cs
c
2
1
2
5.4
5
2/520
R
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Avoiding Boundaries for Sampling Rates
Practically avoid sample rates on boundaries due to
Non-ideal analog bandpass filters
Sample rate clock generator instabilities and
Slight imperfections in available A/D converters
Keep a guard band to cater for non-ideal filters
Another intermediate sampling
frequency choice possible
where modd is an odd integer
s.t. fs> 2B 14
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Optimum sampling rates
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Reading Sections
Understanding DSP (Lyons)Chapter 2 : Periodic SamplingSections:
2.3 (covered in lecture)2.4 (for your interest)
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