The reel project aims at improving analog tape simulators in software, and tries to discover whether it is feasible to develop a simulator that really closely mimics the ‘reel thing’.
This time we’ll shed some light on the most sought-after properties of tape – it’s non-linear behavior, also referred to as tape compression, tape saturation, tape warmth and alike. You may intuitively think that tape saturation or compression is just some static input/output function with some variable ‘softness’, but as you will read in this post, such a simple process will never be able to accurately simulate the effect of analog tape recording.
As we have seen in the previous post on magnetic tape recording, the spectrum of a signal changes as a result of tape recording. This change, however, is both level and frequency dependent. This can be observed very clearly if we measure the tape transfer function on the same recorder with different signal input levels.
This picture shows the measured frequency transfer function for a slow tape speed (3.75IPS) for two different signal levels that are 15 dB apart. The red curve represents a higher signal level, the blue curve a lower signal level. As can be seen, for higher input levels, high-frequencies are compressed (attenuated), while low-frequencies are not influenced much. Thus, tape saturation is a frequency and level dependent process.
Modulations and asperity noise
A well-known effect of tape recording is wow and flutter, resulting from tape speed variations across time. Technically, these effects result in frequency modulations. The frequency modulations can be observed by computing the tape output spectrum for a single frequency input, as shown here.
The figure does not show a single peak at the original input frequency (1kHz), but shows several side bands resulting from frequency and amplitude modulations. These modulations are in fact not only caused by tape speed variations, but are also the result of inhomogeneities in the tape oxide coating, presence of dust particles and other stochastic influences. The modulations caused by such inhomogeneities are often referred to as asperity or modulation noise. The effect of asperity noise is clearly audible for sine tones, and gives tape recording a very distinct and unique character. Some interesting real-world examples of this effect can be auditioned here. From the spectrum plot above, we can not determine if certain side bands result from frequency or amplitude modulations, but fortunately for the tape simulation efforts, we can use the Hilbert transform to separate amplitude from frequency modulations. The results of this analysis are beyond the scope of this post, but it has become very clear that both amplitude and frequency modulation spectra have to be reproduced very accurately to achieve a convincing asperity noise simulation.
Aliasing or intermodulation distortion?
This is an interesting picture. It shows the spectrum of the recording of a 16kHz tone. As you can clearly see, besides the 16kHz tone, there’s also a peak in the spectrum at about 3500 Hz. In a digital world you may think this is the result of aliasing distortion. But it is not. Tape uses an inaudible, high-frequency bias signal (typically around 100 kHz) to improve the linearity of the tape resonse. This signal is added to the signal that is stored on tape. The nonlinear behavior of the tape results in intermodulation distortion of the 16kHz input tone and the bias frequency, in this example resulting in a distortion component popping up at 3500 Hz.
Putting it all together
As has been outlined so far, analog tape recording imposes a variety of ‘effects’ that are being superimposed on the audio signal:
- Tape noise or hiss, with a particular spectrum and frequency-dependent statistical dependence;
- Spectral changes, induced by the tape, the recorder, and the read head (the head bump);
- Compression/saturation, with strong level and frequency dependencies;
- Amplitude and frequency modulations, for example resulting in wow, flutter, and asperity noise;
- Intermodulation distortion resulting from interacting signal components and bias signals; and
- Other effects not discussed here, such as hysteresis loops, tape dropouts, head azimuth adjustment, under or overbiasing, non-linearities in the electronic ciruitry, etc.
To complicate things even further, these properties are highly dependent on the recorder unit design, its settings/calibration, and the tape itself.
Some initial simulation results
The big question obviously is whether we can simulate all of the above effects accurately, and if so, whether the result sounds like tape. You can judge for yourself based on the audio excerpts below. Each audio player object below contains 5 versions of a short audio excerpt:
- Original, unprocessed file;
- Real Studer Revox A77mk4 recording (7.5IPS);
- Simulated Studer Revox A77mk4 recording (7.5IPS);
- Real Teac A4300SX recording (7.5IPS);
- Simulated Teac A4300SX recording (7.5IPS)
All recordings and simulations were done at relatively hot signal levels to more clearly express non-linear behavior.
Listen closely to the saturation effects, and how background noise levels modulate with the instruments (for example with the kick drum).
To have a fair, unbiased trial, the simulations and real tape recordings have randomly been labeled (A) and (B). Can you figure out which is real and which is simulated in the excerpts below?
Audio excerpt 1
Audio excerpt 2
Audio excerpt 3
Audio excerpt 4