Sculptor: A Real Time Phase Vocoder
Computer music in some respects places extreme demands on operating systems, especially now that inexpensive desktop platforms have enough raw processing power to perform relatively complex signal processing tasks in real time. Shared memory and System V IPC are powerful allies in realising audio manipulation tools under real-time control. Sculptor is a set of tools for Linux which uses these techniques to produce impressive throughput, even on modest platforms. It was initially conceived as a research tool, but may end up being a musical instrument.
This is the story of how a program, which ran in batch mode on PDP-11s taking many hours to produce a few seconds of audio output, can now be run in real time on an inexpensive desktop Linux machine. Changing a program from batch mode to real time presents an enormous challenge to the programmer: the user interface becomes an issue, imposing a completely new structure on the software, as user-interface-originated events need to be processed asynchronously with the real-time audio synthesis.
Timbre means sound colour, a perceptual correlate of harmonic content, in the same way that pitch is related perceptually to frequency. A violin and a flute can be played at the same pitch and loudness, but always have different timbre. One process which computer-musicians like to use is morphing, where sound can be altered smoothly from an initial timbre to a finishing one. Many readers will be familiar with the process of video morphing and will appreciate how it is an entirely different process from simply cross-fading. One method of achieving the audio equivalent is to manipulate the audio signal not as a series of time samples, but as a series of evolving spectra. By changing the attributes of the sound's spectrum as it evolves, this and many other interesting effects can be made.
In this article, a method for manipulating spectra in real time and providing continuous audio output will be examined. An example xview application has been written, so anybody with those libraries and an appropriate sound card can experiment for themselves.
The phase vocoder is one of the more powerful methods of manipulating sounds in the frequency domain. It is not a new technology; MIT's CSound application (see Resources), which was ported to the C language and UNIX from the original MUSIC11 program written in assembler for the PDP-11 minicomputer by Barry Vercoe, contains phase vocoder software. However, the algorithm was of such complexity and computers at the time were so short of processing power it would often require many hours of processing to realise each second of audio output. Only recently has sufficient processing power reached the desktop to make real-time phase vocoding a viable proposition.
A vocoder is an electronic signal processor consisting of a bank of filters spaced across the frequency band of interest. Originally, it was hoped such a device would be able to reduce the bandwidth necessary for the transmission of voice telephony, but it rapidly found other applications in popular music. A voice signal could be analysed by the filter bank in real time, and the output applied to a voltage-controlled filter bank or an oscillator bank to produce a distorted reproduction of the original. The effect can be heard in some Electric Light Orchestra tracks, and in the theme music to the film Educating Rita.
After Michael Portnoff (see Resources) demonstrated an efficient method of building the required filter banks digitally, the door was open for a computer-based implementation of a digital phase vocoder, bringing with it a vast number of possibilities for the analysis, manipulation and synthesis of audio. Wishing to use this technology to improve my understanding of the relationship between a sound's timbre and its spectrum, I set about writing Sculptor, a real-time and interactive phase vocoder for Linux.
The Phase Vocoder in Sculptor comes in two parts: a batch-mode analyser called analyse, and a real-time synthesiser called, perhaps more imaginatively, prism. analyse reads an input file in Sun/NeXT audio format. The sample rate we use most often is 22,050 samples per second, as my P120 machine at home can comfortably keep up with this resynthesis rate using floating-point arithmetic with enough power left over to see to the work of running the X Window System interface. Samples can be acquired in the usual way using a command-line recording tool, but finding that rather tedious, we wrote Studio (see Resources) in Tcl/Tk to make the process of acquiring short samples more accessible.
analyse reads the sample file and breaks it up into overlapping windows of about 10ms in length. This window length was chosen because evidence suggests the ear is insensitive to spectral changes on a shorter time scale. Each window is Fourier-transformed, producing an array of spectral samples (see Figure 1), but instead of simply storing the amplitude and phase of each Fourier result (bin), the amplitude and phase change per window are recorded.
To understand why the phase change per window is important rather than the absolute phase, let's consider a simple example. Suppose we are using a sample rate of 8192Hz and have a 128-point FFT. Each window will last approximately 15ms, and the spacing between Fourier bins will be 64Hz. Now present this program with a sine wave at 1KHz. The Fourier transform cannot represent this signal exactly; recall that it is behaving like a bank of filters 64Hz apart, so the nearest filter frequencies will be bins 15 and 16 at 960 and 1024Hz, respectively.
When this same signal is analysed a quarter of a window later, it will still be represented as a 1024Hz sine wave. Since its frequency is actually lower, it will appear to have lagged in phase. By storing the phase change per window, sufficient information is retained to at least approximate the original 1000Hz sinusoid by overlapping the inverse Fourier transformation results and adding them together at resynthesis time.
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