Comb filtering is often a challenging subject to cover and understand, but its effects are significant when recording and mixing, so it is very much a topic that is worth learning about both theoretically and with respect to experiencing how sounds change when they are subject to comb filtering. Before discussing comb filtering in detail, we should first recap on the concept of frequency cancellation (sometimes referred to as phase cancellation), which is the foundation and cause of comb filtering.
Frequency cancelation and phase cancellation
Frequency and phase are audio topics that deserve considerable discussion in their own right, but one key consideration is when signals that are summed (also mixed or added) together cause cancellations and unwanted modifications to the resultant sound. Frequency cancellations occur when we add two identical signals together when one has been delayed by a period of time. The figure below shows this in a simple block-diagram form:
In the recording studio or mixing room, there are many occasions where we might accidentally delay a sound signal and then later mix it together with another version of itself (that is either not delayed, or delayed by a different amount). In reality, time delays are impossible to avoid, since they occur in the following scenarios:
- When the same sound source is recorded by two different microphones that are at different distances from the source
- When the same sound source is recorded by two microphones that have different internal sound response and conversion characteristics
- When a sound wave is reflected off a surface in the studio and hence captured twice (or more as an echo or reverberation) into a single microphone
- When a recorded signal is split in a mixing desk (for example sent to an auxiliary channel for reverb or other processing) and then mixed back with the original signal
- When a recorded signal is split in a DAW software package and processed differently (for example, one version is sent to an effects plugin whereas the original is not), and then later mixed back together
- Multiple combinations and permutations of the above scenarios acting together!
Summed sine wave cancellation
To give a simple sine wave example, total frequency cancellation occurs when the delayed sine wave is shifted by exactly the amount of time that causes a ‘180-degree phase offset’. By this we mean that the signal has been delayed such that all the positive points in the original signal are mirrored and negative in the delayed signal. Since a sinewave repeats after 360 degrees, we see that total cancellation occurs when we add two sine waves together when one is shifted by 180 degrees, as shown in the figure below:
It’s possible to calculate what time delays cause 180-degree shifts for different frequency sinewaves. For example, a 100 Hz sinewave has 100 complete cycles per second, so each cycle takes 10 ms (or 0.001 seconds). A 180-degree offset is at exactly half a cycle (because one cycle is 360 degrees), so the 100 Hz sinewave will cause frequency cancellation if it is mixed with another 100 Hz sinewave that has been delayed by 5 ms. Using the same maths, we see that 200 Hz signals are cancelled when one of the two signals has a 2.5 ms time delay, and 500 Hz signals cancel when one of the sine waves has a 1 ms time delay. These kind of time delays (0-20 ms) are very common in modern recording scenarios for those reasons given in the bullet-point list above.
Frequency cancelation as comb filtering
So, now we’ve covered the basics of frequency cancelation, it’s worth asking how does frequency or phase cancelation relate to comb filtering? And what exactly is comb filtering?
Well, comb filtering refers to the fact that in a more complex signal, such as white noise, music or some other audio recording, frequency cancelation occurs at many different frequencies all at the same time, and this can cause huge differences to the sound that we hear when comb filtering is present. Here’s the technical explanation…
The duration of the delay determines which frequencies are cancelled and which aren’t. For example, a 2 ms delay means that a sine wave of cycle period 4 ms will cause cancellation (because 2 ms is 180 degrees of a 4 ms wave). A 4 ms period sine wave has a frequency of 250 Hz, because 250 waves with a period of 4 ms can occur in 1 second (i.e. 1000 ms). But a 2 ms delay causes more than one frequency to be cancelled, because of the repetitive nature of a sine wave, so we see a similar cancellation effect for the 2 ms delay at 750 Hz, 1250 Hz, 1750, Hz and so on. The effect of a 2 ms delay also doubles the frequency content at perfectly in-phase frequencies such as 500 Hz, 1000Hz, 1500 Hz etc. This can also be evaluated on the same signal for a different time delay. For example, for a 6 ms delay, the frequencies of cancellation are 83 Hz, 249 Hz, 415 Hz, 588 Hz and so on. This effect of phase cancelation is known as comb filtering because multiple frequencies are filtered out and the subsequent frequency spectrum resembles a hair comb, as shown in the diagram below.
Experience the sounds of comb filtering
You can experience the sound of comb filtering in a digital audio workstation with a signal generator plugin and a delay plugin. To do this in Logic Pro, for example, setup an audio channel with the Test Oscillator inserted and set to a White Noise source, as in the image below. Now send the signal to an auxiliary bus with a 0 dB level. You now have two versions of the same white noise signal playing at the same time.
Add a sample delay to the auxiliary channel and add a 1 sample delay to the auxiliary channel. You should be able to hear the difference in the sound of the noise signal with the delayed version added in. Now increase the number of samples delayed to 2, 3, 4, 5 and so on, each time notice the difference in sound when the sample delay changes. The sound you hear with the delayed auxiliary channel incorporated is the sound effect caused by comb filtering. If you have access to a good spectrum analyser plugin, open this up on the master channel and you will be able to see the comb filtering in action too.
Now switch off the test oscillator and add an audio file to the source channel. You can now implement the sample delay on the auxiliary again and hear how the sound of a recording is affected by comb filtering.
Comb filtering used in phaser and flanger audio effects
It’s interesting to note that phaser and flanger audio effects use the principle of comb filtering to produce a novel and creative sound effect. Phaser and flanger effects electronically create comb filtering and then slowly change the time delay to move the cancellation up and down through the frequency spectrum, giving a ‘sweeping’ or ‘phasing’ sound to the audio. This explains why the sound of real-world comb filtering and phase cancellation differs to the phaser processing effect, because in unwanted cancellation, the time delay stays constant, so the sweeping sound is not present.
It’s well worth knowing the scenarios that can cause comb filtering and learning to recognise the sound and results of comb filtering and frequency cancelation in general. The issues of cancelation and comb filtering can be significant for all instruments, but in terms of drums and other low-frequency sounds, cancelation can cause awesome sounding drums to be captured thin and weak in a recording session. If you don’t know what to listen out for then it may be too late to fix adequately when it comes to the mixing session!
If you want to know more about the underlying science of drumheads and drum sound, and learn more creative approaches to drum sound and drum tuning, check out the free iDrumTune ‘Drum Sound and Drum Tuning’ course at www.idrumtune.com/learn
Author Professor Rob Toulson is an established musician, sound engineer and music producer who works across a number of different music genres. He is also an expert in musical acoustics and inventor of the iDrumTune Pro mobile app, which can be downloaded from the App Store links below: