Wordpress | Filter the function wp_get_archives() so a category_id can be added

wp_get_archives() with cat_id

/*
 * Filter the wp_get_archives() so a cat_id can be added
 * Example: wp_get_cat_archives('type=monthly&format=option&show_post_count=1', 46);
 * in this case '46' = the category id
 */

add_filter('getarchives_where', 'custom_archives_where', 10, 2);
add_filter('getarchives_join', 'custom_archives_join', 10, 2);

function custom_archives_join($x, $r) {
  global $wpdb;
  // $cat_ID = $r['cat'];
  $cat_ID = isset($r['cat']) ? $r['cat'] : ''; // prevents 'Notice: Undefined index: cat 
  if (isset($cat_ID)) {
    return $x . " INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id) INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)";
  } else {
    return $x;
  }
}

function custom_archives_where($x, $r) {
  global $wpdb;
  // $cat_ID = $r['cat'];
  $cat_ID = isset($r['cat']) ? $r['cat'] : ''; // prevents 'Notice: Undefined index: cat 
  if (isset($cat_ID)) {
    return $x . " AND $wpdb->term_taxonomy.taxonomy = 'category' AND $wpdb->term_taxonomy.term_id IN ($cat_ID)";
  } else {
    $x;
  }
}

function wp_get_cat_archives($opts, $cat) {
  $args = wp_parse_args($opts, array('echo' => '1')); // default echo is 1.
  $echo = $args['echo'] != '0'; // remember the original echo flag.
  $args['echo'] = 0;
  $args['cat'] = $cat;

  $tag = ($args['format'] === 'option') ? 'option' : 'li';

  $archives = wp_get_archives(build_query($args));
  $archs = explode('</'.$tag.'>', $archives);
  $links = array();

  foreach ($archs as $archive) {
    $link = preg_replace("/='([^']+)'/", "='$1?cat={$cat}'", $archive);
    array_push($links, $link);
  }
  $result = implode('</'.$tag.'>', $links);

  if ($echo) {
    echo $result;
  } else {
    return $result;
  }
}

Hello, why is this not working now? Please tell me how to fix?