class backup_migrate_filter_compression extends backup_migrate_filter {
  var $op_weights = array(
    'backup' => 100,
    'restore' => -100,
  );

  /**
   * This function is called on a backup file after the backup has been completed.
   */
  function backup($file, &$settings) {
    return $this->_backup_migrate_file_compress($file, $settings);
  }

  /**
   * This function is called on a backup file before importing it.
   */
  function restore($file, &$settings) {
    return $this->_backup_migrate_file_decompress($file);
  }

  /**
   * Get the form for the settings for this filter.
   */
  function backup_settings_default() {
    $options = $this->_backup_migrate_get_compression_form_item_options();
    return array('compression' => isset($options['gzip']) ? 'gzip' : 'none');
  }

  /**
   * Get the form for the settings for this filter.
   */
  function backup_settings_form($settings) {
    $form = array();
    $compression_options = $this->_backup_migrate_get_compression_form_item_options();
    $form['file']['compression'] = array(
      "#type" => count($compression_options) > 1 ? "select" : 'value',
      "#title" => t("Compression"),
      "#options" => $compression_options,
      "#default_value" => $settings['compression'],
    );
    return $form;
  }

  /**
   * Return a list of backup filetypes.
   */
  function file_types() {
    return array(
      "gzip" => array(
        "extension" => "gz",
        "filemime" => "application/x-gzip",
        "backup" => TRUE,
        "restore" => TRUE,
      ),
      "bzip" => array(
        "extension" => "bz",
        "filemime" => "application/x-bzip",
        "backup" => TRUE,
        "restore" => TRUE,
      ),
      "bzip2" => array(
        "extension" => "bz2",
        "filemime" => "application/x-bzip",
        "backup" => TRUE,
        "restore" => TRUE,
      ),
      "zip" => array(
        "extension" => "zip",
        "filemime" => "application/zip",
        "backup" => TRUE,
        "restore" => TRUE,
      ),
    );
  }

  /**
   * Get the compression options as an options array for a form item.
   */
  function _backup_migrate_get_compression_form_item_options() {
    $compression_options = array("none" => t("No Compression"));
    if (@function_exists("gzencode")) {
      $compression_options['gzip'] = t("gzip");
    }
    if (@function_exists("bzcompress")) {
      $compression_options['bzip'] = t("bzip2");
    }
    if (class_exists('ZipArchive')) {
      $compression_options['zip'] = t("Zip", array(), array('context' => 'compression format'));
    }
    return $compression_options;
  }

  /**
   * Encode a file with gzip.
   */
  function _backup_migrate_gzip_encode($source, $dest, $level = 9) {
    $success = FALSE;
    if (@function_exists("gzopen")) {
      if (($fp_out = gzopen($dest, 'wb' . $level)) && ($fp_in = fopen($source, 'rb'))) {
        while (!feof($fp_in)) {
          gzwrite($fp_out, fread($fp_in, 1024 * 512));
        }
        $success = TRUE;
      }
      @fclose($fp_in);
      @gzclose($fp_out);
    }
    return $success;
  }

  /**
   * Decode a file with gzip.
   */
  function _backup_migrate_gzip_decode($source, $dest) {
    $success = FALSE;
    if (@function_exists("gzopen")) {
      if (($fp_out = fopen($dest, 'wb')) && ($fp_in = gzopen($source, 'rb'))) {
        while (!feof($fp_in)) {
          fwrite($fp_out, gzread($fp_in, 1024 * 512));
        }
        $success = TRUE;
      }
      @gzclose($fp_in);
      @fclose($fp_out);
    }
    return $success;
  }

  /**
   * Encode a file with bzip2.
   */
  function _backup_migrate_bzip_encode($source, $dest) {
    $success = FALSE;
    if (@function_exists("bzopen")) {
      if (($fp_out = bzopen($dest, 'w')) && ($fp_in = fopen($source, 'rb'))) {
        while (!feof($fp_in)) {
          bzwrite($fp_out, fread($fp_in, 1024 * 512));
        }
        $success = TRUE;
      }
      else {
        $error = TRUE;
      }
      @fclose($fp_in);
      @bzclose($fp_out);
    }
    return $success;
  }

  /**
   * Decode a file with bzip2.
   */
  function _backup_migrate_bzip_decode($source, $dest) {
    $success = FALSE;
    if (@function_exists("bzopen")) {
      if (($fp_out = fopen($dest, 'w')) && ($fp_in = bzopen($source, 'r'))) {
        while (!feof($fp_in)) {
          fwrite($fp_out, gzread($fp_in, 1024 * 512));
        }
        $success = TRUE;
      }
      else {
        $error = TRUE;
      }
      @bzclose($fp_in);
      @fclose($fp_out);
    }
    return $success;
  }

  /**
   * Encode a file with Zip.
   */
  function _backup_migrate_zip_encode($source, $dest, $filename) {
    $success = FALSE;
    if (class_exists('ZipArchive')) {
      $zip = new ZipArchive;
      $res = $zip->open($dest, constant("ZipArchive::CREATE"));
      if ($res === TRUE) {
        $zip->addFile($source, $filename);
        $success = $zip->close();
      }
    }
    return $success;
  }

  /**
   * Decode a file with Zip.
   */
  function _backup_migrate_zip_decode($source, $dest) {
    $success = FALSE;
    if (class_exists('ZipArchive')) {
      $zip = new ZipArchive;
      if (($fp_out = fopen($dest, "w")) && ($zip->open($source))) {
        $filename = ($zip->getNameIndex(0));
        if ($fp_in = $zip->getStream($filename)) {
          while (!feof($fp_in)) {
            fwrite($fp_out, fread($fp_in, 1024 * 512));
          }
          $success = TRUE;
        }
      }
      @fclose($fp_in);
      @fclose($fp_out);
    }
    return $success;
  }

  /**
   * Compress a file with the given settings.
   * Also updates settings to reflect new file mime and file extension.
   */
  function _backup_migrate_file_compress($file, $settings) {
    switch ($settings->filters['compression']) {
      case "gzip":
        $from = $file->push_type('gzip');
        if (!$success = $this->_backup_migrate_gzip_encode($from, $file->filepath(), 9)) {
          $file = NULL;
        }
        break;

      case "bzip":
        $from = $file->push_type('bzip2');
        if (!$success = $this->_backup_migrate_bzip_encode($from, $file->filepath())) {
          $file = NULL;
        }
        break;

      case "zip":
        $filename = $file->filename();
        $from = $file->push_type('zip');
        if (!$success = $this->_backup_migrate_zip_encode($from, $file->filepath(), $filename)) {
          $file = NULL;
        }
        break;
    }
    if (!$file) {
      _backup_migrate_message("Could not compress backup file. Try backing up without compression.", array(), 'error');
    }

    return $file;
  }

  /**
   * Decompress a file with the given settings.
   * Also updates settings to reflect new file mime and file extension.
   */
  function _backup_migrate_file_decompress($file) {
    $success = FALSE;

    switch ($file->type_id()) {
      case "gzip":
        $from = $file->pop_type();
        $success = $this->_backup_migrate_gzip_decode($from->filepath(), $file->filepath());
        break;

      case "bzip":
      case "bzip2":
        $from = $file->pop_type();
        $success = $this->_backup_migrate_bzip_decode($from->filepath(), $file->filepath());
        break;

      case "zip":
        $from = $file->pop_type();
        $success = $this->_backup_migrate_zip_decode($from->filepath(), $file->filepath());
        break;

      default:
        return $file;
        break;
    }

    if (!$success) {
      _backup_migrate_message("Could not decompress backup file. Please check that the file is valid.", array(), 'error');
    }
    return $success ? $file : NULL;
  }
}

backup_migrate_backup_migrate_filters in sites/all/modules/ulmus/backup_migrate/includes/filters.inc

Implementation of hook_backup_migrate_filters().