Basic Digital Signal Processing: Delays

Basic delay-lines (echoes) can be used for a variety of signal-processing techniques, including flanging, comb-filtering and spatialization tricks.

Links

There aren't all that many good 'tutorial' links about basic delays, flanging, etc. because the concepts aren't all that difficult to understand. Some of the more math/theory links may be good if you want to get seriously into delays.

Basic Delays:

Sound Effects Tutorial page -- really basic description of delay effects
Delay -- good introduction from the Harmony Central folks
McGill class page -- a bit more on the mathematics of delay lines

Comb Filters:

McGill class page -- same article as above, but this link goes directly to the "comb filter" section
UC-Santa Cruz page -- from Peter Elsea, see towards the bottom
Stanford article -- mathematics of comb filters from Julius Smith

Flanging:

flanging article -- another good one from Hamony Central
Zen Audio Project -- very simple explanation, audio examples (but I couldn't get them to work with my browser)
McGill class page -- good intro to the math

Applications and Examples

Here are the delay, echo, flanging and comb-filtering examples (plus a few more!) done in class:

week5a-examples.sit -- StuffIt archive with the class max/msp and rtcmix patches

individual patches as text files (for Windows users)
- delay1.txt
- DEL1.sco
- DELAY.sco
- COMBIT.sco
  
  NOTE: the "DEL1.sco", "DELAY.sco" and "COMBIT.sco" files contain the rtcmix scripts used in the "delay1.txt" patch. You will need to download all of them.
- delay2.txt
- delay3.txt
- PANECHO.sco
  
  NOTE: the "PANECHO.sco" file contains the rtcmix script use in the "delay3.txt" patch. You will need to download both.

The following is from a demo done for a potential landscape/soundscape project, showing the absolute joy of delays used with some simple wavetable instruments:

cascade-demo.sit -- StuffIt archive with the max/msp/rtcmix patch

the text files (for Windows users)
- cascade.txt
- cascade.sco
- cascadePE.sco
  
  NOTE: the files "cascade.sco" and "cascadePE.sco" contain the rtcmix scripts used in the "cascade.txt" patch. You will need to download all of them.

The concept of a digital-delay line is fundamental for many digital signal processing techniqes. Delays and echo algorithms can be used for a wide range of effects -- we built and demonstrated a few in class. Very short recirculating delays create "comb filters", or ringing filters that impart a definite pitch to an incoming signal (the psychoacoustic aspects of this phenonemon are somewhat interesting). A moving comb filter is generally called a 'flanger' for those fascinating Beatles-like historical reasons.

Very short delay times between the speakers can create the impression of a sound localization rather than an echo or comb filter effect. This is because our Cognitive Apparatus (oh that Cognitive Apparatus!) uses time differences between our ears to place a sound source relative to our position. Hey, millions of years of evolution can't be wrong. This called the Haas effect, otherwise known as the "precedence effect". This can be exploited in room-simulation or mixing contexts..

Be careful when using the max/msp delay instruments not to confuse specification of delay times in samples with the specification in milliseconds. And of course RTcmix does it even differently, using plain-old-regular seconds to set delay times.

We didn't explore the idea of chaining delays in series or running them in parallel too much. This might be fun to try. The RTcmix PANECHO instrument does a simple two-delay recirculating chain (I've included an example demo patch using PANECHO above).

In some of the literature about delay lines and comb filters, you may encounter references to "feedforward" vs. "feedback" delay lines. We'll be talking about these concepts when we explore the marvelous world of digital filter theory in a few short weeks.