Twitter, as a form of social media, is fast emerging in recent years. Users are using Twitter to report real-life events. This paper focuses on detecting those events by analyzing the text stream in Twitter. Although event detection has long been a research topic, the characteristics of Twitter make it a non- trivial task. Tweets reporting such events are usually overwhelmed by high flood of meaningless "babbles". Moreover, event detection algorithm needs to be scalable given the sheer amount of tweets. This paper attempts to tackle these challenges with EDCoW (Event Detection with Clustering of Wavelet-based Signals). EDCoW builds signals for individual words by applying wavelet analysis on the frequency-based raw signals of the words. It then filters away the trivial words by looking at their corresponding signal auto- correlations. The remaining words are then clustered to form events with a modularity-based graph partitioning technique. Experimental studies show promising result of EDCoW. We also present the design of a proof-of-concept system, which was used to analyze netizens' online discussion about Singapore General Election 2011.