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A DSP TECHNIQUE FOR GENERATING SINUSOIDAL SIGNAL WITH INSTANTANEOUS FREQUENCY AND PHASE ADJUSTMENTS

IP.com Disclosure Number: IPCOM000007053D
Original Publication Date: 1993-Oct-01
Included in the Prior Art Database: 2002-Feb-21
Document File: 3 page(s) / 120K

Publishing Venue

Motorola

Related People

Chin Pan Wong: AUTHOR [+3]

Abstract

This paper describes the construction of a free running oscillator derived horn a recursive digital filter structure. In addition, it is shown that with modifications to the structure, it can change the fre- quency and phase ofthe tone either instantaneously or/and continuously.

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MOTOROLA INC. Technical Developments Volume 20 October 1993

A DSP TECHNIQUE FOR GENERATING SINUSOIDAL SIGNAL WITH INSTANTANEOUS FREQUENCY AND PHASE ADJUSTMENTS

by Chin Pan Wong, Leo Dehner and Kareen J. White

INTRODUCTION:

  This paper describes the construction of a free running oscillator derived horn a recursive digital filter structure. In addition, it is shown that with modifications to the structure, it can change the fre- quency and phase ofthe tone either instantaneously or/and continuously.

When comparing this method to other tone gen- erating methods, three advantages can be seen.

1) it avoids table storage and interpolation ofthe points in between look-up values;
2) within the Nyquist sampling limit, it can gener- ate any frequency tone with specified start-up phase;
3) after the tone generator is started, modification to both the frequency or phase can be easily achieved by manipulating theryfeedback states of the filter structure.
4) No hardware smoothing filter is required since the generated sample is already exact.

STRUCTURE OF THE FILTER:

Signal

Analog Tone

?jLn

sin [ Wc (n + 2) T]

) D/A

sin (W-2 (n + 1)Tj

sin [WC nT]

A = 2 cos(Wc T)

B=-1.0

T = 1 / Fs Fs is the

sampling rate

136 CT Motorola. 1°C. ,993

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0 M

MOTOROLA INC. Technical Developments Volume 20 October 1993

If we express the above block diagram in the form of difference equation, we have

y (n + 22) = A y (n + 1) - y (n)

y (n + 1) and y (n) are related as follows.

If y(n) = sin (0) then y (n + 1) = sin (B + WC T).

To determine the sign, we can use the approximation dfdt [sin WC t] = WC cos WC t

If we use the first order difference operation as the approximation for the derivative tidt, signof{sin[Wc(n+l)T+4]-sinwcnT+#]}or
sign of { y (n + 1) - y (n)} (1) determines the sign ofcos [WC (n + 1) T + 41.

For the special case when y (n + 1) and y (n) are equal (i.e. cos WC t = 0),
we may use the sign of{ y (n) - y (n - l)}. Indeed, if the sampling rate is much higher than the frequency of the tone, equation (1) is a good approximation for WC a cos [WC n T + $1. Therefore, cos [WC (n T + 41 can be approximated

by [Y (n + 1) - Y OWWc. Same method can be used...