reg+LUT

(sinetable) reg

r

phase ACC

mr

r

DAC AIF

signal (re)construction

num controlled osc (NCO)

n

fc fc

systemclock

fc

D

PT: phasetruncation

AQ: amplitude quantization

frequencytuning word

signal

f/fc = D/2^r

digital part:

mixed/analog part:

load

reference part:

(sine)

numerical distortions

Overlappedmodulation structure

Overlappedmodulation structure

Overlapped harmonic structure

Overlapped harmonic structure

Spurious spectralcomponents due to finite word length effects

Spurious spectralcomponents due to finite word length effects

numericalfrequency

r = phase ACC register length ( frequency resolution )

m = memory (LUT) address length ( phase resolution )

n = data width ( amplitude resolution)

0 256 512 768 1024160

120

80

40

0signal and spurs

Frequency (bin)

Rela

tive

leve

l (dB

V)

dBk

k

r = 11, m = 7,without AQ, D = 150

0 256 512150

100

50

0

dBk

k

r =10, m = 10n = 12, D = 32

P = 2r / gcd(D, 2r) = 32 ( sample period )No. of the AQ-spurs: (P/4) - 1 = 7E = 2r-m / gcd(D, 2r-m) = 8 ( period of the phase error )

No. of the PT-spurs: E - 1 = 7

0 256 512 768 1024160

120

80

40

0signal and spurs

Frequency (bin)

Rela

tive

leve

l (dB

V)

dB2k

k

r = 11, m = 7,with AQ: n = 12, D = 150

No. of the AQ-spurs: (P/4) - 1 = 255

Same as above, i.e. there are

no PT - spurs because E = 1 at the specific D tuning word

r =10, with PT: m = 7,n = 12, D = 32

Prolog to an Internet link ...

An example of interaction between PT and AQ :zero-phase sine, 8K FFT, BH7 (7-term Blackman-Harris) window, without and with AQ

Online interactive ( Mathcad ) simulations and movie clips:

http://www.hit.bme.hu/people/papay/sci/DDS/simul.htm

Online interactive ( Mathcad ) simulations and movie clips:

http://www.hit.bme.hu/people/papay/sci/DDS/simul.htm

ACRONYMS

DDS: Direct Digital SynthesisNCO: Numerically Controlled Oscillator ACC: accumulatorLUT: Look-Up TableDAC: Digital-to-Analog ConverterAIF: Anti-Imaging Filterreg: registergcd: greatest common divisorPT: Phase TruncationAQ: Amplitude Quantization*FFT: Fast Fourier TransformFPGA: Field Programmable Gate ArrayDDC: Digital Down ConverterDUC: Digital Up ConverterSDR: Software Defined RadioARB: arbitrary

harmonically related cos components

with -5dB level change (and 8K FFT, BH7 window)

There is a simple procedure for evaluating the spur structures due to numerical distortion in a single-tone DDS.

*

There is a simple procedure for evaluating the spur structures due to numerical distortion in a single-tone DDS.

*Determining the location and the level of spursis a good starting point for the NCO designor selection ( e.g. parameterization of an NCO core in FPGA ).

*In digital communication systems there are several applications that do not convert the numerical samples into an analog signal :

digital radios and modems, software-defined radios, digital down/up converters.

*

Interactive simulation helps to discover the composed spectral maps for specific applications and tuning ranges ( spurs vary rather irregularly with tuning ),

proves to be a usable tool for multi-tone ( DDS-based ARB waveform generators ).

Interactive simulation helps to discover the composed spectral maps for specific applications and tuning ranges ( spurs vary rather irregularly with tuning ),

proves to be a usable tool for multi-tone ( DDS-based ARB waveform generators ).

Spectral purity is one of the most important specifications to the signal synthesis.

*

email: papay@hit.bme.hu

An example of multi-tone :

PT - spurs : AQ - spurs :

( D is all two in hexa, E = 65 536 ) ( P = 2 147 483 648 )