Stanford Research Systems SR780, Operating Manual And Programming Reference

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User Math Functions 2-51
SR780 Network Signal Analyzer
FFT1 and 800 point FFT1 stored in a Trace) can be combined in an User Function. The
math is performed over the longest operand with the shorter operand array being used in
a circular fashion. This usually leads to meaningless results.
Measurement operands (FFT(1), Time(1), etc.) and Traces have an X axis type, either
frequency or time domain. Arrays of frequency data start at the lowest frequency. Arrays
of time data start at time=0. A frequency domain operand (FFT(1)) can be added to a
time domain operand (Time(1)) point by point even though the result is meaningless. The
X axis type of a User Function is determined by examining its equation from left to right
and keeping track of domain switching (IFFT and FFT) operations. Operand terms with
an incompatible X axis type have no effect on the function’s X axis type, though the
entire equation is still evaluated.
Constants are simply constant for each point. They also have no effect on the function’s
X axis type. If a User Function is defined simply in terms of constants (no other
operands), then the X axis type defaults to frequency.
If a User Function’s X axis type or length is determined by a Trace, then changing the
data in the Trace may change the function’s X axis type or length as well.
Operations
Operands are combined with Operations to define a function.
Arithmetic operations (+, -, x, /) combine operand terms on a point by point basis. It is
the user’s responsibility to ensure that the operand terms have the correct X axis type and
lengths required to produce meaningful results.
View operations ( Mag( ), Mag
2
( ), Phase( ), Real ( ), Imag( ) ) simply convert the
complex operand array into the desired form. Mag( ) and Mag
2
( ) compute the magnitude
(
√
(x
2
+ y
2
)) or magnitude squared (x
2
+ y
2
) with a real result. Phase( ) computes the phase
(tan
-1
( y/x )) unwrapped with a real result. Real( ) simply zeroes the imaginary part.
Imag( ) copies the imaginary part to the real part and then zeroes the imaginary part.
Conj( ), Ln( ), Exp( ) and Sqrt( ) are defined as follows,
Conj(x + jy) = x - jy
Conj(x - jy) = x + jy
Ln(x + jy) = ln(r) + j
θ
Exp(x + jy) = exp(x) • ( cos(y) + jsin(y) )
Sqrt(x + jy) =
√
r • ( cos(
θ
/2) + j sin(
θ
/2) )
[X/(1-X)](x + jy) = (x + jy)/(1 - x - jy)
where r =
√
(x
2
+ y
2
) and
θ
= tan
-1
( y/x ). Sqrt computes all angles positive from 0. The
[X/(1-X)]( ) operator is generally used on real arguments only.
The jOmega( ) operator is simply j
ω
and zeroes the real part and fills the imaginary part
with the value of
ω
(2
π
• frequency) at each point in the array. The frequency is
determined by the span of the operand. A measurement operand (FFT(1) or Time(1)) uses
the current frequency span. A Trace operand uses the span of the measurement which is
stored in the Trace. The DC (0 Hz) bin is filled with 1/16 of the value of the first point (to
avoid divide by zero).