DOC.
30
QUASIPERIODIC
PROCESSES
305
00
+00
f
I
(x)
sin(x
-
y)°
dx
=
/(y)fmadu
=
TTl
(y).
0
X
y
CO
^
Taking
this into
account,
one
obtains,
by
later
exchanging
x
for
y
in the result
oo
I(x)
=
-
f
\|r(A)cos(^A)rfA,
...(5)
TT
^0J
which
equation,
in
conjunction
with the
previous equations
iJf(A) =
x(A)
-
x(°°)
•••(4)
T
X(A)
=
\
/F(t)F(t +
A)A,
...(2)
0
solves the task
set.
It would be much
too
wearisome
to
carry
out
a
purely
computational
evaluation
[p.
4]
of the
integrals given
in
(2)
and
(4)
for
many
values of the
argument A
or x.
It
would be advisable
to construct
mechanical
devices for
carrying
out
these
squaring
operations.
In
particular,
it
should be
possible
to
build
a
device that
solves
a
problem
of which the
integration given
in
(2)
is
only
a
special
case.
I
have in mind
a
device
that solves
the
following problem.
Let
F(t)
and
O(t)
be
two
empirically given
functions. One has
to
find the
quantity
T
®
F(t)P(t)dt
o
using
a
mechanical
device.[4]
Such
a
device could also be used
to determine the
function
T
0(A)
=
f
F(t)P(t
+
A
)dt,
0
which
permits
one
to decide whether
or
not
there
is
a
causal connection between the
two
quantities
F and
0.
If there
is
no
causal
connection,
then
0
is
independent
of
A; if, on
the
other
hand,
there is
a
causal
connection,
then
0(A)
will be
a
function with
an
extremum.
Based
on
the value of
A
to
which this extremum
belongs,
one
will also obtain
information
on
the
nature
of this causal connection.
In
closing,
I
wish
to
express my
thanks
to
my
former
colleague
G. Pick[5]
for
several remarks due
to
which the
presentation
of this
topic
has
been
substantially
simplified.