dsp lecture 18

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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Lecture Outline

Sampling of Bandpass signals(taken from Understanding DSP by Lyons)

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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

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2''

m

Bff cs

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7/16Lectures 18 EE-802 ADSP SEECS-NUST

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



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



Optimum sampling rates

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16/16L t 18 EE 802 ADSP SEECS NUST

Reading Sections

Understanding DSP (Lyons)Chapter 2 : Periodic SamplingSections:

2.3 (covered in lecture)2.4 (for your interest)

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dsp lecture 18

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