CEDAR's first version of the "Azimuth Corrector" was called the Phase/Time Corrector, and ran on the CEDAR-2 Production System, an early PC-based suite of processes that ran under DOS. This was developed primarily for the broadcast and video industries, for whom mono compatibility is of great concern. The name was, however, misleading because the software did not correct "phase" errors within the signal. It corrected timing errors.

The next incarnation of the process was implemented in the AZ-1 Azimuth Corrector, a CEDAR Series 2 rackmount unit. The reason for the change of name - despite the functionality remaining broadly unchanged - was purely a marketing decision. Audio engineers knew what azimuth errors were, and the unwanted side effects that they created.

Unfortunately, the use of the term "azimuth" implies that these errors only occur when analogue tape recorders are involved in the signal chain. This is not the case. Indeed, timing errors can occur whenever the two signal paths in an analogue, stereo signal path, are inconsistent with each other. They can even occur - although to a lesser extent - if the pick-up cartridge in a turntable is mis-aligned. Nevertheless, this is the name that makes most sense to the world at large, and that is why the AZX+ is called an Azimuth Corrector rather than a stereo timing corrector.

To understand what these timing errors do to a signal, let us first consider some simple cases involving just sinewave oscillators.

A sinewave oscillator can be described in its entirety by just three parameters: its frequency, amplitude, and phase. The frequency and amplitude describe, to a good approximation, the perceived pitch and volume of the signal. The phase, however, is of no audible significance until we combine more than one such sinewave.

For the moment, let us consider two sinewaves of the same frequency and amplitude, but different phases. Figure 1 shows a simple sinewave climbing away from 'zero' at T=0. The figure also shows another, identical waveform with identical phase (i.e. starting at the same time). As you would imagine, the two waveforms add together to produce the same sound, but louder.

Figure 1: Summing two sine waves

But now consider figure 2. This also shows a simple sine climbing away from 'zero' at T=0, with another, identical waveform offset by 1/2 of its cycle. If we add these two waves together, they cancel each other out, and we hear nothing. Although, in isolation, both oscillations sound identical, combining them results in silence.

Figure 2: Summing two out-of-phase sine waves

This is a very simple result, and demonstrates perfect addition and perfect cancellation. These can also be represented by the Lissajous diagrams shown in figure 3 (in phase), and figure 4 (out-of-phase).

Figures 3 and 4: Lissajous representations of in-phase and out-of-phase signals

If you combine the waveforms with other delays (i.e. at different phases) you get other results that lie between the maximum volume and silence. What's more, if, instead of combining these waves into a single signal, you output them through different speakers, you hear a different result. When the signals are in phase you hear the original tone, perfectly reproduced in mono. But as the phase shifts, you hear the tone shift across the sound field. (Figure 5.)

Figure 5: Phase changes shift the perceived source of the signal

Of course, the relationship between the phase shift and the timing error is defined by the frequency of the signal. If the sinewave frequency increases or decreases, a given timing difference will lead to different relative phases between the signals. This concept then leads to the following situation.

Consider two complex signals, such as those that represent music or speech. Fourier analysis tells us that these can be represented by an infinite number of sinewaves that represent all the frequencies present in the signal. So, for any given timing difference between the left and right channels, each sinewave in the signal will be phase-shifted by a different amount. Some will be added together and thus become louder, most will be smeared across the stereo image, and some will (if reproduced in mono) cancel out entirely. The result, when viewed on a spectral analyser, looks exactly like a broad comb-filter, with the distance between the "teeth" of the comb defined by the size of the timing error. (Figure 6).

Figure 6: Phase changes generate comb-filtering

It is the distortion of the phase relationships and the consequent filtering effect that causes all the audible problems of timing errors. These include loss of high frequencies, muddy bass, poor mono compatibility, and a general smearing of the stereo image. Worse still, if the timing error is not precisely constant, you will hear a "flanging" effect caused by the "teeth" of the comb filter sweeping backwards and forwards through the spectrum.

Audio engineers have traditionally employed a range of processors to hide these deficiencies: equalisers, stereo enhancers, dynamics processors and reverb units. However, none of these attack the heart of the problem - these small but significant non-synchronisations of the left and right channels.

CEDAR corrects these problems by eliminating the timing errors that cause them. It does this by identifying any monophonic component in the stereo sound and then measuring the timing difference between the left and right channels of the signal. If any such error is detected, the system recreates the signals such that they are accurately aligned. The timing measurement is performed nearly 50 times a second, and the signal is corrected dynamically according to each of these measurements. Zipper noise and digital glitching are avoided by regenerating the signal with an accuracy of 1% of a sample. Furthermore, a sophisticated filter minimises the chance that the detector will be fooled by unusual signals that contain little or no monophonic components, so that CEDAR should never generate erroneous corrections and introduce phase/time errors of its own. However, should you wish to apply a timing correction of your own choosing, a manual mode allows you to do so.

There is one other use for CEDAR's phase/time correction products, and this is related to broadband noise reduction. If you transcribe a monophonic signal held on analogue tape or disc using a stereo tape-head or cartridge, you will create two monophonic signals. Each of these will contain the desired signal, and some noise If you then add time-align these channels and sum them to mono using CEDAR, you will generate a monophonic signal in which the desired signal is 6dB louder than either of the individual channels, but in which the broadband noise content may be as little as 3dB louder. (This is a consequence of the random nature of broadband noise.) As a result, you have given yourself head start of (up to) a 3dB increase in signal-to-noise ratio before you attempt noise reduction on the signal.

Note about tape-head azimuth errors:

When you retrieve the sound from a stereo tape that has either been recorded off-azimuth or replayed off-azimuth, there are two sources of degradation occurring.

The first effect is caused by the distance - in the direction of tape travel - between the centres of the tape heads. This is the primary timing difference, and it is this that CEDAR's processes detect and correct.

The second effect is the smearing caused by the length of tape covered - again in the direction of tape travel - by the offset head. In general terms, the head will then 'average' the signal lying underneath it at any point rather than measuring the instantaneous value. The degradation caused by this will be smaller than that caused by the primary error, and the effect will therefore be less significant. However, it will always lead to a pronounced loss of high frequency content, and to a small reduction in dynamic content.