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Dsp implementation

As you begin to implement your PLL on the DSP, it is highly recommended that you implement and test your NCO block firstbefore completing the rest of your phase-locked loop.

Sine-table interpolation

Your NCO must be able to produce a sinusoid with continuously variable frequency. Computing values of θ n on the fly would require a prohibitive amount of computation and program complexity; a look-up table is a betteralternative.

Suppose a sine table stores N samples from one cycle of the waveform: k k 0 N 1 2 k N . Sine waves with discrete frequencies ω 2 N p are easily obtained by outputting every p th value in the table (and using circular addressing). The continuously variable frequency of yourNCO will require non-integer increments, however. This raises two issues: First, what sort of interpolation should be used to get the in-betweensine samples, and second, how to maintain a non-integer pointer into the sine table.

You may simplify the interpolation problem by using "lower-neighbor" interpolation, i.e., by using the integerpart of your pointer. Note that the full-precision, non-integer pointer must be maintained in memory so that thefractional part is allowed to accumulate and carry over into the integer part; otherwise, your phase will not be accurateover long periods. For a long enough sine table, this approximation will adjust the NCO frequency with sufficientprecision. Of course, nearest-neighbor interpolation could be implemented with a small amount ofextra code.

Maintaining a non-integer pointer is more difficult. In earlier exercises, you have used the auxiliary registers( ARx ) to manage pointers with integer increments. The auxiliary registers are not suited for thenon-integer pointers needed in this exercise, however, so another method is required. One possibility is to performaddition in the accumulator with a modified decimal point. For example, with N 256 , you need eight bits to represent the integer portion of your pointer. Interpret the low 16 bits of theaccumulator to have a decimal point seven bits up from the bottom; this leaves nine bits to store the integer partabove the decimal point. To increment the pointer by one step, add a 15-bit value to the low part of the accumulator,then zero the top bit to ensure that the value in the accumulator is greater than or equal to zero and less than256. How is this similar to the addition modulo 2 discussed in the MATLAB Simulation ? To use the integer part of this pointer, shift the accumulator contents seven bits to theright, add the starting address of the sine table, and store the low part into an ARx register. The auxiliary register now points to the correct sample in thesine table.

As an example, for a nominal carrier frequency ω 8 and sine table length N 256 , the nominal step size is an integer p 8 N 1 2 16 . Interpret the 16-bit pointer as having nine bits for the integer part, followed by a decimal point and sevenbits for the fractional part. The corresponding literal (integer) value added to the accumulator would be 16 2 7 2048 . If this value were 2049, what would be the output frequency of the NCO?


You may want to refer to Proakis and Blahut . These references may help you think about the following questions:

  • How does the noise affect the described carrier recovery method?
  • What should the phase-detector look like for a BPSK modulated carrier? (Hint: You would need to considerboth the in-phase and quadrature channels.)
  • How does α affect the bandwidth of the loop filter?
  • How do the loop gain and the bandwidth of the loop filter affect the PLL's ability to lock on to acarrier frequency mismatch?

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Ece 320 spring 2004. OpenStax CNX. Aug 24, 2004 Download for free at http://cnx.org/content/col10225/1.12
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