How to sort posts in Alphabetical order

So here’s the widget code I’m using to display posts. Even though I changed the $sort_by to title from date it’s still loading posts in order by date. Anyone know what I need to do to load them alphabetically?

<?php class CategoryPosts extends WP_Widget {

	function __construct() {
		$widget_ops = array('classname' => 'cat-post-widget', 'description' => __('List single category posts'));
		parent::__construct('category-posts', __('Category Posts'), $widget_ops);
	}

	// Displays category posts widget on blog.
	function widget($args, $instance) {
		global $post;
		$post_old = $post; // Save the post object.

		extract( $args );

		$sizes = get_option('mkrdip_cat_post_thumb_sizes');

		// If not title, use the name of the category.
		if( !$instance["title"] ) {
			$category_info = get_category($instance["cat"]);
			$instance["title"] = $category_info->name;
		}

		$valid_sort_orders = array('date', 'title', 'comment_count', 'rand');
		if ( in_array($instance['sort_by'], $valid_sort_orders) ) {
			$sort_by = $instance['sort_by'];
			$sort_order = (bool) isset( $instance['asc_sort_order'] ) ? 'ASC' : 'DESC';
		} else {
			// by default, display latest first
			$sort_by = 'title';
			$sort_order = 'DESC';
		}

		// Get array of post info.
		$cat_posts = new WP_Query(
			"showposts=" . $instance["num"] .
			"&cat=" . $instance["cat"] .
			"&orderby=" . $sort_by .
			"&order=" . $sort_order
		);

		// Excerpt length filter
		$new_excerpt_length = create_function('$length', "return " . $instance["excerpt_length"] . ";");
		if ( $instance["excerpt_length"] > 0 )
			add_filter('excerpt_length', $new_excerpt_length);

		echo $before_widget;

		// Widget title
		if( !isset ( $instance["hide_title"] ) ) {
			echo $before_title;
			if( isset ( $instance["title_link"] ) ) {
				echo '<a href="' . get_category_link($instance["cat"]) . '">' . $instance["title"] . '</a>';
			} else {
				echo $instance["title"];
			}
			echo $after_title;
		}

		// Post list
		echo "<ul>\n";

		while ( $cat_posts->have_posts() )
		{
			$cat_posts->the_post(); ?>