The ARITHMETIC MENU is poorly named, but is meant to convey the idea
that the included operations *combine* amplitudes in the arrays pixel
by pixel in some way. In all cases, the result is saved in array f_{1}
and f_{2} is cleared. The primary array (*i.e.,* the "first"
array for order-sensitive processes such as subtraction, division, correlation,
the lookup table, and raising to a power) is the array most recently processed;
the other may be selected by typing the appropriate number for that array.
When dividing, pixels divided by "0" are assigned the value "0".
In the list below when the order of the arrays affects the result, f_{a}
and f_{b} refer to the primary and secondary array, respectively.

**+** **ADD arrays: f _{1}[n]
= f_{1}[n] + f_{2}[n]; f_{2}[n]
= 0**

**- SUBTRACT arrays:
f _{1}[n]
= f_{a}[n] + f_{b}[n]; f_{2}[n]
= 0**

**x MULTIPLY arrays: f _{1}[n]
= f_{1}[n] x f_{2}[n]; f_{2}[n]
= 0**

**/ DIVIDE arrays: f _{1}[n]
= f_{a}[n] / f_{b}[n]; f_{2}[n]
= 0**

*** CONVOLVE
arrays: f _{1}[n]
= f_{1}[n] _{*} f_{2}[n];
f_{2}[n]
= 0**

**& CROSSCORRELATION: f _{1}[n]
= f_{a}[n] & f_{b}[n]; f_{2}[n]
= 0**

**> SHIFT AND ADD: f _{1}[n]
= f_{a}[n] + f_{b}[n - n_{0}]; f_{2}[n]
= 0**

**T LOOKUP TABLE: f _{1}[n]
= f_{b}{f_{a}[n]};
f_{2}[n] = 0**

**^ RAISE TO POWER: f _{1}[n]
= {f_{a}[n]}^{f_{b}[n]}; f_{2}[n]
= 0**

The uses for most of these operations are obvious. However, note that the order of the arrays is critical when computing the Correlation, Lookup Table, and Power operations. The order of the arrays may be exchanged to give array 1 or 2 "priority" by typing the appropriate number. The convolution and correlation operations are computed via FFTs, and will yield outputs that are periodic over N samples.

The lookup table option [T] is used to apply a tone-transfer characteristic
(such as a photographic characteristic curve) to the amplitudes of the
samples. This is useful for demonstrating the effect of a nonlinear transfer
characteristic on the spectrum of the signal. To use the lookup table,
first scale the amplitudes of the input array f_{a} to the interval
[-1,+1]; the normalization option ([Z] in the OPERATIONS MENU may be used).
The lookup table is generated in f_{b} with the amplitudes also
scaled to the interval [-1,1]. The x-coordinate of the lookup array f_{b}
is scaled during processing -- the samples with the smallest and largest
index are mapped to -1 and +1, respectively, in the lookup operation.

The Power option [^] takes the nth sample of the complex amplitude of
the first array and raises it to the complex amplitude of the nth sample
of the second array. This operation also may be performed by computing
the complex LOG of the first array (option [G} in the OPERATIONS MENU),
multiplying the two arrays together (option [x] in the ARITHMETIC MENU),
and applying the result as the exponent + *i* in exp( + *i* )
(option [E] in the OPERATIONS MENU). Though this is a more general operation
than raising to a constant complex power (option [^] in the OPERATIONS
MENU), it is not commonly used.

RETURN to OVERVIEW of SIGNALS MANUAL

OPTIONS in MAIN MENU

OPTIONS in FUNCTIONS MENU
**(suggest that "Image Autoload" be turned off!)
** OPTIONS in OPERATIONS MENU