Filters are just functions which transform input to an output. However filters need to be Dependency Injected. To achieve this a filter definition consists of a factory function which is annotated with dependencies and is responsible for creating a filter function.

// Filter registration
function MyModule($provide, $filterProvider) {
  // create a service to demonstrate injection (not always needed)
  $provide.value('greet', function(name){
    return 'Hello ' + name + '!';
  });

  // register a filter factory which uses the
  // greet service to demonstrate DI.
  $filterProvider.register('greet', function(greet){
    // return the filter function which uses the greet service
    // to generate salutation
    return function(text) {
      // filters need to be forgiving so check input validity
      return text && greet(text) || text;
    };
  });
}

The filter function is registered with the $injector under the filter name suffix with Filter.

it('should be the same instance', inject(
  function($filterProvider) {
    $filterProvider.register('reverse', function(){
      return ...;
    });
  },
  function($filter, reverseFilter) {
    expect($filter('reverse')).toBe(reverseFilter);
  });

For more information about how angular filters work, and how to create your own filters, see Filters in the Angular Developer Guide.