Proc. of the 17th Int. Conference on Digital Audio Effects (DAFx-14), Erlangen, Germany, September 1-5, 2014 SHORT-TIME TIME-REVERSAL ON AUDIO SIGNALS Hyung-Suk Kim Julius O. Smith CCRMA, CCRMA, Stanford University Stanford University Stanford, CA, USA Stanford, CA, USA
[email protected] [email protected] ABSTRACT 2. FOURIER ANALYSIS In this section, we define STTR and perform a Fourier transform We present an analysis of short-time time-reversal on audio sig- to study its effects in the frequency domain. nals. Based on our analysis, we define parameters that can be used to control the digital effect and explain the effect each parameter has on the output. We further study the case of 50% overlap-add, 2.1. Short-Time Time-Reversal then use this for a real-time implementation. Depending on the x(t) w(t) window length, the effect can modify the output sound variously, Let be the input signal and be the window function of L R from adding overtones to adding reverse echoes. We suggest ex- length with constant overlap-add for step size : (Equation 2.1) ample use cases and digital effects setups for usage in sound design 1 X and recording. w(t − mR) = 1 (2.1) m=−∞ The STTR signal y(t) is formed by the following steps. 1. INTRODUCTION Step 1. Window the input signal x(t) with w(t − mR). Overlap-add (OLA) methods are widely used in digital audio ef- Step 2. Reverse the signal under the window: fects. Examples include time stretching, pitch shifting, phase vocoder, and more complex effects based on the short-time Fourier trans- (a) Move the windowed signal to the origin.