Here is one approach:

#! perl
use Modern::Perl;
use Data::Dump;

my @array1 =
(
     undef,
     undef,
    'abcd',
    'efgh',
     undef,
     undef,
    'jklm',
    'nopq',
     undef,
     undef,
);

my @array2 = split /\0\0/, join('', map { $_ // "\0" } @array1);
   @array2 = @array2[1 .. $#array2] unless $array2[0];    

dd @array1;
dd @array2;
[download]

Output:

21:38 >perl 508_SoPW.pl
(
  undef,
  undef,
  "abcd",
  "efgh",
  undef,
  undef,
  "jklm",
  "nopq",
  undef,
  undef,
)
("abcdefgh", "jklmnopq")

21:38 >
[download]

Update 1: The above assumes that “blank” means undef. If it means '' (the empty string), then change the expression:

map { $_ // "\0" } @array1
[download]

to

map { $_ || "\0" } @array1
[download]

map { $_ eq '' ? "\0" : $_ } @array1
[download]

30^th January, 2013. Amended to address the problem noted by The Perlman, below.

Update 2: As with muba’s solution below, the above assumes that the array begins with a double blank.

Hope that helps,