Patent GB-851596-A (GB)
Title: Improvements relating to interpolating apparatus
Inventor: VOLES ROGER
IPC: G06G7/30
Filed: 1956-01-14
Abstract: 851,596. Electric analog calculating. ELECTRIC & MUSICAL INDUSTRIES Ltd. Jan. 8, 1957 [Jan. 14, 1956], No. 1332/56. Class 37 Interpolating apparatus comprises interpolating means adapted to respond to a set of at least three reference signals representing values of a function for values of the independent variable of the function which are separated by intervals bearing a predetermined ratio to produce interpolated signals representing values of the function for further intermediate values of the variable, combined with means for deriving, from a set of applied signals representing reference values of the function for values of the independent variable separated by intervals having a different ratio, reference signals representing modified values of the function for values of the variable separated by intervals which are in said first predetermined ratio, and applying said modified signals to said interpolating means. Three input signal voltages x 1 , X, X  3  representing functions of a variable parameter t =(-1), T, (+1) are applied to a quadratic interpolator of the kind described in Specification 796,994 comprising (Fig. 2) a tapped autotransformer 10 whose terminals 11, 12 are energized by voltages X 1 , X 3  and whose taps are respectively connected over quadratically graduated windings 15a to 15g to a linear subinterpolator 13 comprising a slow speed switch arm engaging successive pairs of adjacent contacts connected to the respective plactransformer taps in accordance with equally spaced values of variable t, to excite a linearly tapped autotransformer engaged by the arm of a high speed switch geared to the low speed switch arm to select interpolated values of x at terminal 14. Winding 15d is connected from the mid tap of transformer 10 to the central low speed switch contact. A third voltage X for a value T of variable t is applied to input 17 and is such that the intervals between the successive values of the parameter have a ratio differing from that to which the interpolating device 10, 13, 15 is adapted. The X signal is connected to the returns of auto-transformers 19a, 19b; 18a, 18b; and also to the junction 19a, 19b over winding 15h coupled to windings 15a to 15g with turns equal to winding 15d. The free end of winding 19b is connected to the junction of windings 18s, 18b whose free end is in turn connected to the centre-point of auto-transformer 10 over a winding 20a constituting a further auto-transformer in conjunction with transformer 10. Windings 19a, 18a have fixed numbers of turns while windings 19b, 18b, 20a have numbers of turns variable in conformity with the value of T. The voltage of the centre-point of auto-transformer 10 referred to ground is (X 1  + X 3 /2) and the voltage between the ends thereof is (x 3 - X1) so that the induced voltage in winding 20a is (X 3  - X 1 /2) T and the voltage across AD is X-(X 1  + X 3 /2) - (X 3  - X 1 /2) T =d, the voltage across BD is (d/1 + T) and the voltage across CD is d/(1+T)(1-T) = (d/1-T 2 )  the several transformer windings being appropriately sensed. This voltage appearing across winding 15h is injected into all the interpolating transformer windings 15a to 15g proportionally to their turns, so that the voltage appearing at the junction 16 of winding 15d and linear subinterpolator 13 is X 2 = (X 1  + X 3 /2) + (d/1-T 2 ) which represents (Fig. 1) an input control voltage intercepted between x 1  and x  3  along the t axis such that the three signals have the appropriate equal interval ratio of the abscissal variable for quadratic interpolation by 10, 13, 15; the parameter d being the intercept between the point X on the quadratic interpolation curve X 1  X 2  X 3  and the intersection of the T abscissa with the line joining points X 1  X 3 . In Fig. 3, winding 10 is disposed on toroidal core 21 also carrying four windings 21a to 21d the numbers of whose turns are graduated in successive powers of two with switching 22a to 22d operated by relays 23a to 23d, to which are applied in parallel the pulse code signals of the binary digits, representing the first decimal digit of the value of T derived from a tape record reader. Other similar winding units 24, 25, 26 responsive to the pulse code signals representing the second, third, and fourth decimal digits of the value of T similarly insert corresponding graduated power of two windings on the toroidal core so that the number of effective turns inserted in series represents the operative value of T; the relative senses of the windings and transformer 10 being established by changeover switches 29a, 29b operated by relay 29c responsive to the sign of T. Windings 18b, 19b are similarly variable by relays 23a, 23b, 23c, 23d in response to the value of T, but sensing switches are unnecessary so long as these windings are mutually opposed. Fig. 4 shows a modification of Fig. 2 wherein winding 15h is wound in negative sense to windings 15a to 15g so as to develop a voltage (X 1  + X 3  / 2) - X 2  applied to transformer 30a, 30b feeding transformer 31a, 31b; the latter winding being connected with winding 32a of transformer 32a, 32b in series with the input signal X on terminal 17 and the junction point 16 of the central winding. 15d of 15a to 15g with the linear sub-interpolator 13 developing voltage X2. The numbers of turns of windings 30a, 31a, 15h represent unity, on windings 30b, 31 b, 32a, represent T, and on winding 32b represent duality; the latter being connected across tapped auto-transformer 10. Since the voltage across winding 31b is (X 1 -2X 2 +X 3 ) T 2 /2, across 32a is (x<SP>3</SP>-x 1 ) T/2 and from Fig. 1 X=X 2  + (X 3 -X 1 ) T/2 + (x1 - 2X + x 3 ) -; the voltage x2 developed 2 at point 16 is as before the required value for the appropriate interval ratio of the interpolator. Windings T are variable in accordance with the input coding as shown in Fig. 3. In a further modification (Fig. 5 not shown) operating on similar principles, both the coordinate signals (x,6) of each input point are utilized implicitly; the value x is quadratically interpolated against the value #, each coordinate being a function of time, and the set of three input signals represent the points (# 1 , x 1 ) (#, X) (# 3 , X 3 ) where # 1 , # is not necessarily equal to # # 3 , and the range # 1  to #  3  corresponds linearly to 0 ## t ## 1 with T = [# 1  # / # 1  # 3 ] so that it is shown that The invention is applicable to interpolation apparatus utilizing orders of interpolation higher than quadratic in response to more than three reference signals. Specifications 796,993 and 830,462 are referred to.