Audio timescalepitch modification
Time stretching is the process of changing the speed or duration of an audio signal without affecting its pitch. Pitch scaling or pitch shifting is the reverse: the process of changing the pitch without affecting the speed. There are also more advanced methods used to change speed, pitch, or both at once, as a function of time.
These processes are used, for instance, to match the pitches and tempos of two pre-recorded clips for mixing when the clips cannot be reperformed or resampled. (A drum track could be moderately resampled for tempo without adverse effects, but a pitched track could not). They are also used to create effects such as increasing the range of an instrument (like pitch shifting a guitar down an octave).
The simplest way to change the duration or pitch of a digital audio clip is to resample it. This is a mathematical operation that effectively rebuilds a continuous waveform from its samples and then samples that waveform again at a different rate. When the new samples are played at the original sampling frequency, the audio clip sounds faster or slower. Unfortunately, the frequencies in the sample are always scaled at the same rate as the speed. In other words, slowing down the recording lowers the pitch, speeding it up raises the pitch, and the two effects cannot be separated. This is analogous to speeding up or slowing down an analog recording, like a phonograph record or tape.
- Main article: Phase vocoder
One way of stretching the length of a signal without affecting the pitch is to build a phase vocoder after Flanagan, Golden, and Portnoff.
- compute the instantaneous frequency/amplitude relationship of the signal using the STFT, which is the discrete Fourier transform of a short, overlapping and smoothly windowed block of samples;
- apply some processing to the Fourier transform magnitudes and phases; and
- perform an inverse STFT by taking the inverse Fourier transform on each chunk and adding the resulting waveform chunks.
The phase vocoder handles sinusoid components well, but early implementations introduced considerable smearing on transient ("beat") waveforms at all non-integer compression/expansion rates, which renders the results phasey and diffuse. Recent improvements allow better quality results at all compression/expansion ratios but a residual smearing effect still remains.
The phase vocoder technique can also be used to perform pitch shifting, chorusing, timbre manipulation, harmonizing, and other unusual modifications, all of which can be changed as a function of time.
Rabiner and Schafer in 1978 put forth an alternate solution that works in the time domain: attempt to find the period (or equivalently the fundamental frequency) of a given section of the wave using some pitch detection algorithm (commonly the peak of the signal's autocorrelation, or sometimes cepstral processing), and crossfade one period into another. This is called time domain harmonic scaling or the synchronized overlap-add method and performs somewhat faster than the phase vocoder on slower machines but fails when the autocorrelation mis-estimates the period of a signal with complicated harmonics (such as orchestral pieces). Cool Edit Pro seems to solve this by looking for the period closest to a center period that the user specifies, which should be an integer multiple of the tempo, and between 30 Hz and the lowest bass frequency. For a 120 bpm tune, use 48 Hz because 48 Hz = 2,880 cycles/minute = 24 cycles/beat * 120 bpm.
This is much more limited in scope than the phase vocoder based processing, but can be made much less processor intensive, for real-time applications. It provides the most coherent results for single-pitched sounds like voice or musically monophonic instrument recordings.
High-end commercial audio processing packages either combine the two techniques (for example by separating the signal into sinusoid and transient waveforms), or use other techniques based on the wavelet transform, or artificial neural network processing, producing the highest-quality time stretching.
These techniques can also be used to scale the pitch of an audio sample while holding speed or duration constant.
Note that the technique can be called pitch scaling or pitch shifting, depending on perspective. Under one definition of musical pitch, pitch is defined as the logarithm of frequency; as the musical pitch is shifted linearly (shifting every note up the scale by a perfect fifth, for instance), the frequencies of the signal are actually being scaled, because of the logarithmic relationship between the notes we hear and the actual frequencies of those notes. A frequency shift, which is performed by amplitude modulation, does not preserve the ratios of the harmonic frequencies that determine the sound's timbre, and is not a "musical" transformation. Similarly, a literal pitch scaling, in which the musical pitch is scaled (a higher note would be shifted at a greater interval than a lower note) is highly unusual, and not musical. However, "pitch" can also be used to refer to frequency, and the other two transformations are not commonly used, so either term usually refers to musical pitch shifting.
Time domain processing works much better here, as smearing is less noticeable, but scaling vocal samples distorts the formants into a sort of Alvin and the Chipmunks-like effect, which may be desirable or undesirable. To preserve the formants and character of a voice, you can analyze the signal with a channel vocoder or LPC vocoder plus any of several pitch detection algorithms and then resynthesize it at a different fundamental frequency.
- The Phase Vocoder: A Tutorial - A good description of the phase vocoder
- New Phase-Vocoder Techniques for Pitch-Shifting, Harmonizing and Other Exotic Effects
- A new Approach to Transient Processing in the Phase Vocoder
- PSOLA Synthesis, SOLAFS Synthesis - Two specific methods of time domain TDHS or SOLA processing.
- Audio Engineering Society
- Original E2 article (http://everything2.com/index.pl?node_id=1074923)
- http://www.bdti.com/faq/dsp_faq.htm - comp.dsp FAQ