While reading on compact cassette readers (as part of a preliminary study on digitizing archives) I found out that azimuth, or the angle made between the tape and the reading is a considered a big issue, the best case being an azimuth of exactly 90°. I could not, however, quite find what was the effect of varying that angle, even if pretty much everyone agrees that it somehow lessen the tape’s high frequency response. Let’s see how, exactly.

First, let’s understand how the signal is recorded on the compact cassette. The device uses a pulse-amplitude modulation encoding, or, simply put, an encoding scheme where the value of the signal is directly encoded by the intensity of the magnetism on the tape. Strong positive magnetism yields a large positive value, strong negative magnetism yields a “large” negative value, and the waveform is encoded using variation in strength of the magnetisation on tape. In the figure, red is negative, green positive, and saturation represents intensity.

To give some frequency resolution, the recording/reading head is narrow, but spans the whole width of the track (on a single-track tape, that would be the width of the tape, but as compact cassettes are recorded as four distinct tracks, two for each side). The device reads/writes the magnetism under the head gap. The tape advances continuously, rather than by discrete increments, acting as an interpolation between samples, preventing the introduction of high frequency noise components.

The precision, in terms of frequencies, of the recording is limited by two factors: the width of the gap and the speed of the tape under the head. We have:

$\displaystyle F_{max} \propto \frac{V_{tape}}{W_{gap}}$.

In tape cassettes, constants align so that $F_{max}$ is about 15KHz (or maybe 16KHz). That’s if all goes well.

Since these tape drives contain a lot of moving parts, especially in auto-reverse models, it may happen that the head moves. There are four types of displacementment (in no particular order):

• Height. The track should be centered on its reading head. If it the head is too low, it may even overlap the track below, leading to crosstalk (you pick in a channel sound from another channel) in addition of weakened signal (if you read only 80% of the signal, it will be 20% weaker).
• Wrap. The head gap should be at 90° with the tape. Not sure exactly what the effects would be; probably weakened signal.
• Zenith. The head must touch the tape evenly. If some parts of the head are futher away from the tape, then the signal is weakened. Possibly induces wear on the tape too.
• Azimtuh. The head gap should be perpendicular to the direction of the tape. Effects can include phase shift between channels (as the head is slanted, one track is read earlier (or later) than the other) and high frequency loss.

Plus any random effects like varying tape speed, noise from the environment, crud on the head, etc. This video explains it very well.

Let’s concentrate on azimuth for now.

In the best case, tape flows perpendicular to the head gap:

The head is either completely within a recording cell or is across at most two cells. The value read is simply a weighted average of the two, with proporitions determined by the position of the head. This corresponds to a rectangular window whose width is proportional to the width of the head gap. The box filter in time domain yields a sinc in frequency domain. Applying a convolution with the box time-domaine filter is like multiplying frequencies by the sinc function.

If the head is slanted, then it looks something like this:

If the head is really slanted, then the read head may overlap more than one cell, and the corresponding filter isn’t a box anymore, it’s a trapezoid. If the height is correct, then it’s an isoceles trapezoid. Something like this:

Which is starting to look like a smoothing filter, something that is really bad news for the frequency response of the device.

How much tilt do we need to notice the effect in the sound? What are the spectral properties of the trapezoid filter?

To be continued next week