It's a difficult one as a webpage doesn't have access to the local hardware and therefore doesn't have access to the audio stream.
There are a couple of ways you could work around this:
1. Convert your WPF code to Silverlight code as Silverlight does have access to web cam and microphone resources.
2. Deploy a WPF windows application which does the recognition from the website via ClickOne. Pass any recognised phrases to the web server via a web service and use ajax/postbacks within your website to get access to the phrases. I've used this process for integrating biometrics into a website. To reduce the latency, maintain a permanent AJAX request which the response is held up until the server has a response. It saves the delay introduced by implementing checks on a polling bases. Doing this works well be it's important to consider the web gardening implications and memory requirements of the web server.
ClickOnce Deployment[
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