Use and bind {{input}} inside a component

Sorry if this is a silly question. I am in the middle of the steepest part of the Ember learning curve and trying to get a simple app going as a learning tool for myself, and my google-fu is failing me in understanding how to do this;

I have a component that is basically a list of model objects with some filtering options. The filter option relevant to this discussion is a free-text search. I want to have an {{input}} that is is bound to some value that affects the result list whenever it is updated.

{{input type=text value=filterString}}

In my poor understanding of Ember, I would have bound the value of the input to a string property, and have my filteredMatches computed property depend on that. However, if I define that property as such:

filteredMatches: Ember.computed.filter('matches', 'filterString', function(match, index, array) {

I get an error in the console log:

Uncaught TypeError: callback.call is not a function

If I remove the reference to 'filterString', it works as expected, but of course the filtering is not updated when I type something into the input.

So with my limited knowledge of Ember, I am stuck with this; Is the input actually binding to filterString on the controller, not the component? I do not use explicit controllers as I understand they will be going away. If that is the case, how can I have a computed property in my component depend on a controller property?

If that is not the case (i.e. controllers are not involved), how can I bind the input to a component property and react to value changes accordingly?

ember -v
version: 2.3.0-beta.2
node: 5.6.0
npm: 2.14.10
os: win32 x64

Thanks for any help, and again, sorry if this question is stupid!