Embedding Vars in Double Quotes
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Smarty will recognize assigned variables embedded in "double quotes" so long as the variable name contains only numbers, letters and under_scores. See naming for more detail. 
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With any other characters, for example a period(.) or $object->reference, then the variable must be surrounded by`backticks`.
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In addition, Smarty does allow embedded Smarty tags in double-quoted strings. This is useful if you want to include variables with modifiers, plugin or PHP function results. 
Examples
{func var="test $foo test"}              // sees $foo
{func var="test $foo_bar test"}          // sees $foo_bar
{func var="test `$foo[0]` test"}         // sees $foo[0]
{func var="test `$foo[bar]` test"}       // sees $foo[bar]
{func var="test $foo.bar test"}          // sees $foo (not $foo.bar)
{func var="test `$foo.bar` test"}        // sees $foo.bar
{func var="test `$foo.bar` test"|escape} // modifiers outside quotes!
{func var="test {$foo|escape} test"}     // modifiers inside quotes!
{func var="test {time()} test"}          // PHP function result
{func var="test {counter} test"}         // plugin result
{func var="variable foo is {if !$foo}not {/if} defined"} // Smarty block function
{* will replace $tpl_name with value *}
{include file="subdir/$tpl_name.tpl"}
{* does NOT replace $tpl_name *}
{include file='subdir/$tpl_name.tpl'} // vars require double quotes!
{* must have backticks as it contains a dot "." *}
{cycle values="one,two,`$smarty.config.myval`"}
{* must have backticks as it contains a dot "." *}
{include file="`$module.contact`.tpl"}
{* can use variable with dot syntax *}
{include file="`$module.$view`.tpl"}
Note
Although Smarty can handle some very complex expressions and syntax, it is a good rule of thumb to keep the template syntax minimal and focused on presentation. If you find your template syntax getting too complex, it may be a good idea to move the bits that do not deal explicitly with presentation to PHP by way of plugins or modifiers.
See also escape.