Chapter 5: The Transformation of Sound by Computer

Section 5.5: More on Convolution

Another interesting use of the phase vocoder is to perform convolution. We talked about convolution a lot in our section on reverb (both in the time domain and in the frequency domain).

Soundfile 5.18
Convolution: Schwarzhund

A simple convolution: a guitar power chord (the impulse response), a vocal excerpt, and the convolution of one with the other.

We have sonically turned the singer’s head into the guitar chord: he’s singing "through" the chord.

Remember that a convolution multiplies every frequency content in one sound by every frequency content in another (sometimes called a cross-multiply). This is different from simply multiplying each value in one sound by its one corresponding value in another. In fact, as we mentioned, there is a well-known and surprisingly simple relationship between these two concepts: multiplication in the time domain is the same as convolution in the frequency domain (and vice versa). As you probably saw in Section 5.2, the mathematics of convolution can get a little hairy. But the uses of convolution for transformations of sound are pretty straightforward, so we’ll explain them in this section.

Cross-Synthesis

Convolution is a type of cross-synthesis: a general, less technical term which means that some aspect of one sound is imposed onto another. A simple example of cross-synthesis returns us to the subject of reverb. We described the way that, by recording what is called the impulse response of a room (its resonant characteristics) using a very short, loud sound, we can place another sound in that room (at whatever position we "shot") by convolving the impulse response with that sound. Surprisingly, by convolving any sound with white noise, we can simulate simple reverb.

Using Convolution

Although reverberation is a common application of the convolution technique, convolution can be used creatively to produce unusual sounds as well. Simple-to-use convolution tools (like that in the program SoundHack) have only recently become available to a large community of musicians because up until recently, they only ran on quite large computers and in rather arcane environments. So we are likely to hear some amazing things in the near future using these techniques!

Soundfile 5.19
Noise

Soundfile 5.20
Inhale

Soundfile 5.21
Noise and inhale convolved

In this convolution example, Soundfile 5.19 and Soundfile 5.20 are convolved into Soundfile 5.21. The two sound sources are noise and an inhale.