A Second Order Elliptic Equalizer for Vinyl Mastering

[mediatechnology]

After a lot of poking around and experimenting I think I've gotten a better handle on what goes on with brick-walled material.

Phase rotation in the original source is not the cause. Hyper-compression is.

It appears that hyper-compression induces large amounts of odd-order distortion that, when allpassed (or simply undergoes phase rotation) causes peaks to grow in level.
I confirmed this with a track I hyper-compressed myself and then analyzed using a tool called Mastering Visualizer, "MasVis." http://www.lts.a.se/lts/masvis

MasVis has a display that they call "allpassed crest factor" which they claim is an indirect measure of "crush."
The dashed line is the crest factor of the original file, the second curve the crest factor vs. frequency after allpass.

The following MasVis animation shows THAT's Test Track 37, "Funky Bass" unprocessed, limited 20:1 @-9dB and normalized, and then with two degrees of hyper-compression:


Animation showing THAT's Test Track 37, "Funky Bass" unprocessed, limited 20:1 @-9dB and normalized, and then with two degrees of hyper-compression.

As clipping increases note the spread between the file's crest factor and the allpassed crest factor.

MasVis write:

Allpassed crest factor

This graph probably is the most revealing graph in MasVis. It gives an estimate of how much the crest factor has been lowered by processing of the 2-channel master. In the graph, there are four curves, two red for the right channel, and two blue for the left channel. The dashed line shows the crest factor, ie the same information as above the waveform graphs. The solid line shows the crest factor of the signal after it has passed an allpass filter. This second crest factor is a rough, and typically underestimated value of how large the crest factor was prior to level maximation of the 2-channel master.

At first, it may seem impossible to make such an estimate, but experience shows that the method works. Of course it does not give an exact value of the original crest factor, but it is good enough to tell when the track has been subjected to destructive loudness maximation.

The difference between maximum in the solid line and the dashed line correlates quite well with the amount of crest factor loss that is a result of level maximation of the 2-channel mix.

Here is the method that MasVis uses to make the graph:

1. Draw a dashed line at the crest factor of the track.
2. Run the track through seven different first order allpass filters at 20, 60, 200, 600, 2000, 6000 and 20000 Hz
3. For each of the seven filtered signals, calculate a new crest factor value
4. Plot a solid line representing the crest factors of the seven signals as a function of filter frequency

Apparently, when the odd harmonic artifacts of hyper-compression are phase rotated (or undergo any significant phase shift) the peaks are no longer folded inward but instead fold outward causing an increase in peak level but not an increase in RMS.

I also ran some tests to see what the effects of RIAA pre-emphasis are on brickwalled material.

The peak level increases with brickwalled material are huge when inverse RIAA is applied.

And, as it turns out, MasVis' "allpassed crest factor" measurement correlates well with peak level growth with varying degrees of hyper-compression after inverse RIAA.

I ran the THAT 37 test suite and, sure enough, the original and lightly-limited didn't have the peak growth. The ones with hyper-compression do.
The amount of gain that had to be reduced prior to inverse RIAA correlated closely to MasVis allpassed crest factor.

The allpassed crest factor portion of the graph is small and requires some interpretation due to lack of a scale.
MasVis doesn't have inverse RIAA weighting so some visual fudging is required: The higher the center frequency of the allpassed crest factor the more it underestimated due to HF boost.
But its close.

First I normalized the four tracks downward by 0.25 dB to remove the 0 dBFS clips.
I applied inv RIAA EQ to each track and normalized it downward until I got just under 0 dBFS peaks.

(The unprocessed and limited file did not require normalization.)

The file with "+6 dB slam" required input normalization to -2 to prevent post-EQ clipping.
The +12 dB slam file require normalization to -8 to prevent post-EQ clipping.
For an equal post RIAA EQ peak level the lightly-limited file could be recorded 8 dB hotter than the highly-slammed one.

I can establish that inverse-RIAA'd brickwalled material will overshoot more than identical un-brickwalled material.
Put another way hyper-compressed files require large decreases in record level to maintain the same post-EQ peak level.
This is probably not news to any ME but I needed proof.

What are the consequences of increased peak level from the second-order EE?
Apparently very little after RIAA preemphasis.

Material which has not been brickwalled does not show significant peak level increases.
Files which have been brickwalled do..

The first example are the files with no EE, a second order 300 Hz EE with time delay correction, and a first-order EE.
The expansion in peaks in the second-order example are significant.


Daft Punk Harder Faster Stronger No EE, 300 Hz Second Order, 300 Hz First Order Comparison

When the same three segments are inverse RIAA equalized the differences almost disappear:


Daft Punk Harder Faster Stronger No EE, 300 Hz Second Order, 300 Hz First Order Comparison with Inverse RIAA applied.

The peak levels are:

-1.58 dB in the original
-0.79 dB in the 300 Hz Second-Order EE
-1.62 dB in the 300 Hz First-Order EE

About 0.8 dB more in the second-order EE.
The final difference may be due to the effect of EE which will steer LF Side to Mid.

Even though the second segment in the original looks hotter - and in terms of peak level it is - it is not significantly hotter after Inverse RIAA EQ.

The second-order EE "unwraps" the embedded peak overshoots but the RIAA pre-emphasized output does not have significantly increased peak level.

When inverse RIAA is applied to the output of the second-order EE, whose phase shift is at low frequencies, the peak increase isn't pronounced because LF are highly attenuated on the preemphasis curve.

What I think I might do is provide a means to bypass the "time delay correction" in Mid.
The user could ultimately have it three ways:

1) Single-order
2) Second-order with Mid delay correction (symmetric response)
3) Second-order without correction (asymmetric response)

[ricardo]

I think ANY non trivial EQ will 'unwrap' the 'hidden peaks' in a severely compressed/clipped signal.

The limiting case is MLS as used to test speakers. A long pseudo random sequence .. which is a 2 level digital signal is LP filtered and the result is near Gaussian Random White Noise. Loadsa funky maths about the amount of filtering and the resulting randomness .. but you don't have to do much to get very high Peak/Mean ratios as you would with 'real' GRWN.

I've had to process stuff that was recorded on a smart phone. The original looks like 21st Century 'pop' with a dynamic range of 3dB or less .. being both clipped & compressed by the phones AGC

Just correcting some timbre makes the signal look more like 'real' music with peaks.

Gotta admit this is purely cosmetic as I object to issueing anything that even 'looks' like 21st century 'pop'. Any audible improvement is probably due to my response tweaking. Of course, your all-pass doesn't introduce any frequency response tweaking!

[mediatechnology]

I can't really say that there's any audible improvement from "unwrapping" them.
The clips are just hidden in the waveform.
They look better but that's it.

[mediatechnology]

I wanted to provide another set of visuals to illustrate the self-defeating nature of hyper-compression when the crushed version of the master is used for vinyl.

This test involves applying inverse RIAA EQ and comparing the output RMS and peak levels with varying degrees of processing.

This is a screen capture of THAT Track 37 "Funky Bass" with no processing, limiting at 20:1, 6dB of overdrive (slam) and finally 12 dB of overdrive.
Each of the original files was separately normalized to 0 dB to make them have equal peak level.
The assembled file is normalized to -10 to prevent clipping when Inverse RIAA EQ'd.

Without Inverse RIAA EQ



After Inverse RIAA EQ:



Statistics for the Inverse RIAA Eq'd Files:

Track 37 No Processing:

Peak Amplitude: -12 dB -12.01 dB
Total RMS Power: -32.78 dB -32.78 dB

Track 37 Limiting (20:1 @-9dBFS in original):

Peak Amplitude: -7.55 dB -7.54 dB
Total RMS Power: -28.93 dB -28.93 dB

Track 37 with +6 dB Squash:

Peak Amplitude: -6.01 dB -6.01 dB
Total RMS Power: -26.94 dB -26.94 dB

Track 37 with +12 dB Squash:

Peak Amplitude: 0 dB 0 dB
Total RMS Power: -21.92 dB -21.92 dB

Conclusions:

The first set of files have identical peak level but the RMS values are progressively increased due to limiting.
The second set of files show the RMS progressively increase as a result of compression from -33 dB to -22 dB and the peak levels also increase from -12dB to 0 dB.

The compressed peaks "come back" after Inverse RIAA EQ.

The low crest factor/high RMS waveform in the fourth cut would have to have its overall level - and its RMS values - reduced by 12 dB to produce the same peak level as the first cut.
Putting it another way the first unprocessed cut could be cut 12 dB hotter than the last one - and have 12 dB higher RMS - to produce the same peak modulation.

Compression and limiting is a good thing.
In a preemphasized environment hyper-compression is simply self-defeating.

[ricardo]

I wanted to provide another set of visuals to illustrate the self-defeating nature of hyper-compression when the crushed version of the master is used for vinyl.

Compression and limiting is a good thing.
In a preemphasized environment hyper-compression is simply self-defeating.

But but BUT ... 3dB dynamic range always sounds better (ie louder) on my iThing

Not sure about it being a good thing .. but it's hard to record stuff like rim shots or clap sticks without compression/limiting without an average level your customer will object to.

Who listens to vinyl anyway? Sorry Paul. I'm just jealous cos my vinyl collection is on the other side of the continent and probably will never see the light of day

[emrr]

Eye opening results.

[mediatechnology]

It was surprising.

When you normalize them back the squashed one loses about 1.1 dB RMS.
Not only does it require lower level it's distorted as heck.
I tried some stuff that had higher frequency content and there was some with 2-3 dB RMS gain from being squashed but it wasn't enough to justify squashing it to death.

The vinyl always seems to have higher DR: http://dr.loudness-war.info/

Comparing HDTracks to some of my CD rips of the same release it appears that they are able to get better masters.
http://www.hdtracks.com/

[Gold]

Who listens to vinyl anyway? Sorry Paul. I'm just jealous cos my vinyl collection is on the other side of the continent and probably will never see the light of day

I enjoy making the donuts and fixing the donut maker. I love music but I rarely listen to it for pleasure anymore. One great thing about being in the woods for 10 days without music was that I actually started to miss it. Luckily I've culled the client list so I rarely work on stuff I don't like.

[Gold]

Comparing HDTracks to some of my CD rips of the same release it appears that they are able to get better masters.
http://www.hdtracks.com/

For HD tracks it's doubtful that the CD is the same. I know I generally use the same files for HD tracks as I do for MFiT. They are 24/44.1. I don't have to mash stuff too bad for most things but if I did I'd have to lower the level about 1dB to meet the MFiT spec.

[mediatechnology]

I've given a lot of thought about how to build the second-order elliptic equalizer so that it is as flexible as possible.

My current line of thinking is to have the EE inserted into the existing MS board in the decode path at insert point "F."

By making it part of the MS board, as an option, the balanced MS inserts can still be used ahead of the downstream elliptic EQ.
It's also possible to use insert "C" and perform EE upstream of the MS insert sends.


MS Matrix Block Diagram

The Elliptic Equalizer has three modes:

1) Symmetrical 12dB per octave vertical and crosstalk slopes with Allpass time-correction in mid.
2) Symmetrical 6 dB per octave vertical and crosstalk slopes.
3) Asymmetric with 12 dB per octave vertical and 6 dB per octave crosstalk slope.

Frequency Selection:

On-board Relay-selected frequencies of 75, 150 or 300 Hz.
External stepped switch at customizeable frequencies.


Elliptic Equalizer Block Diagram

I'll post a scan of the Side and Mid filters soon.

Signal Flow:

The Side path consists of two simple cascaded first-order filter selections with relay-selected resistive tuning.

The default frequency is 75 Hz with relays used to select 150 and 300 Hz.
An external four pole stepped switch can also be used.

K1 bypasses Side.
Relay K3 selects the filter slope of 6 dB or 12 dB per octave.
K3B switches the filter outputs.
Because the individual first order sections are tuned to approximately 0.64*Fc, K3A raises the first section's Fc to 75, 150 or 300 Hz when the Side filter is 6 dB per octave.

The Mid path has two cascaded first-order allpass filters to align Mid with Side.
The allpass filter provides symmetrical vertical and crosstalk slopes.

K2 byapsses the allpass under three conditions:
(1) When the EE is bypassed,
(2) When the EE is first-order, or
(3) When the EE is being used to provide an uncorrected, asymmetric, response.

The coil of K2 will be wired so that the allpass filter cannot be engaged unless the EE is in the 12dB/octave mode and not bypassed.

By configuring the elliptic EQ this way its easy to compare first-order to second-order responses on-the-fly.