Time Dilation

🎯 Learning Objectives

By the end of this topic, you should be able to:

Understand the concept of time dilation in audio and its effects on signal duration and pitch.
Differentiate between naive resampling, time-stretching, and pitch-shifting techniques.
Apply time-stretching and pitch-shifting to audio without introducing undesirable artifacts.
Calculate and predict changes in duration and pitch for given time dilation factors.
Explore creative applications of time dilation in sound design, music production, and speech editing.

Introduction:

Time dilation in the context of audio effects refers to the stretching or compression of time-dependent audio signals — that is, altering the perceived duration of a sound without necessarily changing its pitch (or vice versa). It’s a key concept in modern digital audio processing, found in time-stretching, pitch-shifting, delay modulation, and reverberation systems.

Conceptual Overview:

In physics, time dilation describes the stretching of time under relativistic conditions.
In audio processing, the term is metaphorically used to describe temporal manipulation of a signal.
Formally, if an original signal is $x(t)$ a time-dilated version can be expressed as:

𝑦(𝑡)=𝑥(𝛼𝑡)

Where:
$α>1$ → Time compression (signal plays faster)
$α<1$ → Time expansion (signal plays slower)
This transformation changes how quickly samples are accessed during playback.

Time Dilation in Common Audio Effects:

Delay & Echo

The delay line stores audio samples and plays them back after a set time.
Modulating the delay time dynamically causes micro time dilations, perceived as chorus, flanger, or doppler effects.

Example: If delay time changes smoothly over time $𝑇_𝑑(𝑡)$ , the playback head effectively reads samples at a variable rate → creating time dilation artifacts (e.g., pitch glide or Doppler shift).

Reverb (Echo Density & Decay)

Reverberation involves many delayed reflections (impulse responses)
If the system time-scales the impulse response, the perceived room size or reverberation time (RT60) changes
Stretching the IR (time dilation) simulates larger acoustic spaces, while compressing simulates smaller rooms

h′(t)=h(αt)

$α<1$ → longer reverb (large hall)
$α>1$ → shorter reverb (small room)

Time Dilation vs. Pitch Shift:

Operation	Description	Effect on Pitch	Effect on Duration
Naive Resampling	Speeding up or slowing down playback by changing sample rate	Yes (pitch scales with speed)	Yes
Time-Stretching (Independent)	Modifying duration while preserving pitch	No	Yes
Pitch-Shifting (Independent)	Modifying pitch while preserving duration	Yes	No

Applications:

Application	Description
Reverb simulation	Adjusting room impulse response duration
Sound design	Creating slow-motion, dream-like, or elastic soundscapes
Speech editing	Aligning dialogue without pitch distortion
Music production	Beat matching, remixing, time-correcting performances
Film & game audio	Doppler effects for moving sources

Interactive Time Dilation

Time Dilation Factor (0.25x – 4x)

1.00x

Blue: Original waveform | Red: Processed waveform

🧠 Key Takeaways

Time dilation in audio refers to stretching or compressing the duration of a sound, optionally independent of pitch.
Naive resampling changes both time and pitch, while time-stretching algorithms (e.g., granular synthesis, phase vocoder) separate them.
Pitch-shifting modifies pitch without changing duration, using frequency-domain processing.
Applications include slow-motion effects, sound design, speech editing, and music production.
Understanding time dilation helps control temporal perception, rhythm, and creative manipulation of audio signals.

🧠 Quick Quiz:

1) When an audio signal is slowed down using naive resampling, what happens to its pitch?

A) Pitch increases
B) Pitch decreases
C) Pitch remains unchanged
D) Pitch becomes random

2) In independent time-stretching, the duration of the signal changes but the pitch remains the same. Which algorithm type is commonly used for this?

A) FFT phase vocoder
B) Low-pass filter
C) Bitcrusher
D) Reverb tail generator

3) If a sound clip originally lasts 2 seconds and you apply a time dilation factor of 1.5×, what is the new duration?

A) 1.33 s
B) 2.5 s
C) 3.0 s
D) 4.0 s

4) Pitch-shifting up by +12 semitones (1 octave) without changing duration requires:

A) Resampling the audio at half the sample rate
B) Doubling playback speed
C) Frequency-domain pitch processing
D) Increasing the reverberation time

5) Which of the following applications best demonstrates time dilation effects in audio?

A) Echo cancellation
B) Slow-motion sound design
C) Noise gating
D) Equalization

Chapter - 1

Key Words: overviewpipelineaudio processing