First things first, let's get the Firebase CLI installed. You can do this with npm:

npm install -g firebase-tools

Once that's done, you'll need to log in and set up your project:

firebase login
firebase init

When you're initializing, make sure to pick "Functions" and "Storage".

You can either create a new Firebase project or use one you already have. Set it up in your project directory:

firebase init

Choose the options that fit your project, like enabling Cloud Firestore or Storage.

Head over to the functions directory in your project and install the dependencies you need:

cd functions
npm install

Open up index.js in the functions directory. You'll define a Cloud Function to handle files when they're uploaded to Firebase Storage:

const functions = require('firebase-functions');
const admin = require('firebase-admin');
const { Storage } = require('@google-cloud/storage');
const path = require('path');

// Initialize Firebase Admin and GCS
admin.initializeApp();
const storage = new Storage();

exports.processFile = functions.storage.object().onFinalize(async (object) => {
    const filePath = object.name;
    const bucketName = object.bucket;
    const tempFilePath = path.join('/tmp', object.name);

    // Download the file to the local filesystem
    await storage.bucket(bucketName).file(filePath).download({ destination: tempFilePath });

    // Process the file (Example: Convert image to grayscale, extract text, etc.)
    // This part will depend on your specific processing requirements

    // Once processing is complete, upload the file back to a new location on the bucket
    const newFileName = `processed_${object.name}`;
    const newFilePath = path.join(path.dirname(filePath), newFileName);

    await storage.bucket(bucketName).upload(tempFilePath, {
        destination: newFilePath
    });

    console.log(`Processed file uploaded to: ${newFilePath}`);

    // Optionally, delete the temporary file from the local filesystem
    const fs = require('fs');
    fs.unlinkSync(tempFilePath);
});

Time to deploy your function to Firebase:

firebase deploy --only functions

Upload a file to your Firebase Storage bucket and check if the Cloud Function triggers, processes the file, and uploads the processed result to the right spot.

# You can test Firebase via the Firebase Console. Upload a file using the console or any Firebase client libraries to see the function in action.

Make sure you have good logging to debug and trace any issues that pop up during file processing. You can view logs using the Firebase Console or with the Firebase CLI:

firebase functions:log

Optimize your function for performance and cost. Think about things like memory usage, execution timeout, error handling, and retries to make sure everything runs smoothly.

Make sure to set the right permissions for accessing Firebase Storage and Cloud Functions:

# Adjust IAM roles and permissions to secure your Firebase environment