Explain the purpose and usage of decorators in TypeScript.

In TypeScript, decorators are a language feature that allows you to modify the behavior of classes, methods, properties, or parameters at design time. They provide a way to add metadata or modify the structure of the target elements without modifying their original definition. Decorators are extensively used in frameworks like Angular and NestJS to enhance the functionality of classes and their members.

The purpose of decorators is to enable developers to implement cross-cutting concerns, such as logging, validation, authentication, and caching, in a modular and reusable manner. They help in separating these concerns from the core business logic, leading to cleaner and more maintainable code.

Decorators are applied using the `@` symbol followed by the decorator name, which is essentially a function or a class declaration. They can be used on classes, class methods, class properties, or method parameters, depending on the intended usage.

When applied to a class, decorators can be used to:

1. Modify the class behavior: Decorators can wrap the class constructor to add additional functionality or modify the class prototype. For example, the `@Component` decorator in Angular is used to mark a class as a component and enhance it with features like template rendering and dependency injection.
2. Add metadata: Decorators can attach metadata to the class, which can be used for reflection or to provide additional information at runtime. For instance, the `@Serializable` decorator can be used to mark a class as serializable and store metadata about its properties for serialization/deserialization purposes.

Decorators can also be applied to class methods or properties, allowing you to:

1. Modify method behavior: By decorating a method, you can wrap it with additional functionality, such as logging, caching, or access control checks. This can be achieved using decorators like `@Log`, `@Cache`, or `@Authorized`, respectively.
2. Add metadata: Similarly, decorators can be used to attach metadata to methods or properties. This metadata can be utilized by frameworks or libraries to determine how to process or handle these elements. An example is the `@Input` decorator in Angular, which marks a property as an input binding for a component.

Additionally, decorators can be applied to method parameters, enabling you to:

1. Modify parameter behavior: Decorators can wrap method parameters with custom logic, such as validation or transformation. For example, a `@Validate` decorator can be used to validate the input parameters of a method before its execution.
2. Add metadata: Decorators can also be used to attach metadata to method parameters, providing additional information about the expected data or its usage. This metadata can be leveraged by frameworks or libraries to perform automatic dependency injection or to generate API documentation.

Overall, decorators in TypeScript empower developers to extend and customize the behavior of classes and their members without explicitly modifying their implementation. They enable the implementation of modular and reusable cross-cutting concerns, leading to cleaner code organization and increased code maintainability.