Cannot use new with expression typescript

You can't new up an instance. new instanceofAudioContext() isn't a valid thing to do.

Your interface doesn't match the API you're trying to use. In the browser, window.AudioContext isn't a instance of AudioContext. It's the class definition method, typeof AudioContext. You'll also have the same problem with the Function.

If you'd still like to keep your interface. Try this

interface Window {
    AudioContext: typeof AudioContext;
    webkitAudioContext: typeof AudioContext
}

declare var window: Window;

var AudioContextDecl = window.AudioContext || window.webkitAudioContext;
var audioCtx = new AudioContext();

Or if you don't want the interface,

var AudioContextDecl = <typeof AudioContext>(window.AudioContext || window.webkitAudioContext);
var audioCtx = new AudioContext();

Or even just use any. It all transpiles to the same thing.

The problem is that the compiler treats the contextClass variable as an instance of AudioContext while in fact it's merely a constructor function for an AudioContext.

You can simply use any and the compiler will let you new it:

let contextClass : any = window.AudioContext || window.webkitAudioContext;
let context: AudioContext = new contextClass();

Another option would be to introduce a Constructable<T> interface that will let you new up those types:

interface Constructable<T> {
    new(...args: any) : T;
}

interface Window
{
    AudioContext: Constructable<AudioContext>;
    webkitAudioContext: Constructable<AudioContext>
}

let contextClass = window.AudioContext || window.webkitAudioContext;
let context: AudioContext = new contextClass();