Noise and distortion in EQ
Historically
all EQ has suffered from excess noise which has often restricted
its use. Analogue circuits add noise due to transistor (and OPAMP)
noise, thermal and impedance noise and distortion due to linearity
issues. Digital EQ also has mechanisms for adding excess noise and
distortion, but although these are similar in concept to analogue
noise there are important differences. A digital EQ implementation
has the equivalent of finite mathematical precision that sets the
performance limit of the EQ, which is heavily dependent on settings
such as centre Frequency, gain and Q factor. Depending on the specific
design of a digital EQ, precision limit errors may appear as noise,
harmonic distortion and even idling tones, which are both interrelated
and programme dependent.
There are many ways in which errors can crop up in digital EQ and there has been much research and publication of the subject. Many different architectures (algorithms) have been proposed to optimise the situation and they all have advantages and disadvantages depending on the type of EQ and processor intended. In all cases these different algorithms are compromises that trade-off one undesirable effect against another. But with careful design, using appropriate processing and coefficient generation methods, a digital EQ can produce far greater sonic accuracy and measured performance than an analogue design, because being an entirely numerical system it is not dependent on the limitations of imperfect analogue components. One popular method of displaying anomalies in digital systems is the input versus output level plot. In this case we apply a continuously reducing input signal to the device and plot the resulting output level. In a perfect system the plot would be a straight line, as the output would entirely follow the input. The following plot is a comparison of 3 different digital EQ types running on the same hardware platform, with a sine wave input at the EQ resonance frequency.
Both the blue and green plots show aberrations in the responses when the signal reduces. The blue EQ shows that the effect of a competitor EQ plug-in disappears at levels below -80dBFS and the output becomes a distorted version of the input. Considerable harmonic distortion will be apparent at higher levels due to the proportion of the programme signal that these errors represent. The green plot shows the effect of another example EQ plug-in that actually starts to fail to pass any signal at all below around -80dBFS. In other words the programme will go silent at around -90dBFS and very large amounts of harmonic distortion will be present at all levels above that. The purple plot shows the effect of the Sonnox Oxford EQ plug-in under the same conditions and settings, running on the same system platform (the plot is higher because the Sonnox Oxford EQ has higher maximum boost gains than the others). It shows a straight line without any aberrations, which corresponds only with a gain of 20dB at the EQ centre frequency.
The effect of the cramping is to reduce the HF content of the EQ curve,
restricting the openness of the sound and adding to the effect of
harshness due to the predominance of mid frequency action within
the unbalanced EQ curve.
Since this effect is related the closeness to the intended response to the Nyquist frequency, the problem is greatly reduced if the system is run at 2FS (88.2KHz or 96KHz) and this may be part of the reason why over sampled systems are often preferred. But since over sampling the entire system will halve the processing capability of the hardware, this solution is costly in a workstation environment where processing power is at a premium. Some digital EQ designs address this problem by up sampling before the EQ and then down sampling at the output to match the system-sampling rate. But although this is more cost effective than running the whole system at 2FS, the up sampling and down sampling processes are themselves a possible cause of error and quality loss.
By employing novel coefficient generation techniques, the Sonnox Oxford EQ plug-in produces a fully de-cramped and symmetrical EQ response without resorting to inefficient or error prone over sampling techniques. In fact the method also allows the EQ to simulate the responses of an analogue EQ with the centre frequencies above the Nyquist frequency (i.e. 26KHz for the GML option), all at normal base band sampling rates without any change to the performance of the rest of the system.
There are many ways in which errors can crop up in digital EQ and there has been much research and publication of the subject. Many different architectures (algorithms) have been proposed to optimise the situation and they all have advantages and disadvantages depending on the type of EQ and processor intended. In all cases these different algorithms are compromises that trade-off one undesirable effect against another. But with careful design, using appropriate processing and coefficient generation methods, a digital EQ can produce far greater sonic accuracy and measured performance than an analogue design, because being an entirely numerical system it is not dependent on the limitations of imperfect analogue components. One popular method of displaying anomalies in digital systems is the input versus output level plot. In this case we apply a continuously reducing input signal to the device and plot the resulting output level. In a perfect system the plot would be a straight line, as the output would entirely follow the input. The following plot is a comparison of 3 different digital EQ types running on the same hardware platform, with a sine wave input at the EQ resonance frequency.
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| Click to enlarge |
Both the blue and green plots show aberrations in the responses when the signal reduces. The blue EQ shows that the effect of a competitor EQ plug-in disappears at levels below -80dBFS and the output becomes a distorted version of the input. Considerable harmonic distortion will be apparent at higher levels due to the proportion of the programme signal that these errors represent. The green plot shows the effect of another example EQ plug-in that actually starts to fail to pass any signal at all below around -80dBFS. In other words the programme will go silent at around -90dBFS and very large amounts of harmonic distortion will be present at all levels above that. The purple plot shows the effect of the Sonnox Oxford EQ plug-in under the same conditions and settings, running on the same system platform (the plot is higher because the Sonnox Oxford EQ has higher maximum boost gains than the others). It shows a straight line without any aberrations, which corresponds only with a gain of 20dB at the EQ centre frequency.
HF response cramping
Another issue that has differentiated the sound of digital EQs from their analogue counterparts is HF response cramping. This phenomenon occurs when EQ curves approach the HF area closest to the half sampling frequency (Nyquist frequency) and manifests itself as an increase in the steepness of the EQ curve at the upper most part of the response. The following plot shows a comparison between a cramped EQ (red plot) against a conventional EQ (actually a plot of the de-cramped Sonnox Oxford plug-in). |
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| Click to enlarge |
Since this effect is related the closeness to the intended response to the Nyquist frequency, the problem is greatly reduced if the system is run at 2FS (88.2KHz or 96KHz) and this may be part of the reason why over sampled systems are often preferred. But since over sampling the entire system will halve the processing capability of the hardware, this solution is costly in a workstation environment where processing power is at a premium. Some digital EQ designs address this problem by up sampling before the EQ and then down sampling at the output to match the system-sampling rate. But although this is more cost effective than running the whole system at 2FS, the up sampling and down sampling processes are themselves a possible cause of error and quality loss.
By employing novel coefficient generation techniques, the Sonnox Oxford EQ plug-in produces a fully de-cramped and symmetrical EQ response without resorting to inefficient or error prone over sampling techniques. In fact the method also allows the EQ to simulate the responses of an analogue EQ with the centre frequencies above the Nyquist frequency (i.e. 26KHz for the GML option), all at normal base band sampling rates without any change to the performance of the rest of the system.