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{\plain {3X Sinc Resampling with Gaussian
 Interpolation}}
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{\plain {Ken Castleman}}
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{\plain {Jan. 27, 1991}}
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{\plain {Suppose we have a signal}}
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{\plain {and interpolated by}}
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{\plain {The interpolated function is}}
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{\plain {which differs somewhat from\par 
the origonal function in both\par amplitude
 and waveshape. }}
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{\plain Figure 3-11}
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{\plain {Even though the function is oversampled
 (s = 0.3 cycles per sample), interpolation
 with a Gaussian interpolation function 
(display spot) does not give a good reconstruction.}}
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{\plain {We can improve the interpolation
 process by resampling the function at a
 3X higher sampling density. The hard way
 to do this is to perform the origonal sampling
 at a higher sampling frequency. An easier
 way is to create two new sample points 
between each pair of existing sample points
 by interpolating them with sin(x)/x. Since
 the function is oversampled to begin with,
 the result is the same.}}
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{\plain {The interpolation coefficients 
must be normalized to sum to 1.0 so that
 areas of constant amplitude will be preserved.}}
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{0:Sum}NAME={0}?_n_u_l_l_
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{\plain {Interpolation fills in the new 
"synthetic" sample points.             }}
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.EQN 4 0 63 0
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.EQN 5 -18 16133 0
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0 0 1 0 6 0 1 
0 0 1 0 0 0 1 
4 0 6 0 NO-TRACE-STRING
0 1 6 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 32 22 0 3 
.EQN 0 41 16134 0
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0 0 1 0 6 0 1 
0 0 1 0 0 0 1 
0 0 6 5 NO-TRACE-STRING
0 1 6 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 35 22 0 3 
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{\plain (b)}
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Cg a11.000000,54.500000,12
{\rtf1\ansi \deff1
{\fonttbl
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{\plain Figure 3-12}
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.TXT 4 -39 69 0
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{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Courier;}
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{\plain (a) {Notice how this sampled function
 looks easier to interpolate.}}
}
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{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Courier;}
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{\plain (b) {Notice how this interpolated
 function more closely resembles the origonal
 waveshape.}}
}