Digital IIR Inverse RIAA filter 1kHz @ 0 dB Audacity Nyquist

Any Nyquist mathematicians out there able to help me out in creating an inverse RIAA IIR command that can be plugged into Audacity's Nyquist prompt? The sampling frequency is 96 kHz, and it needs to have 1 kHz with 0 dB gain.

I've been playing around with the Wayne Stegall program, but either it doesn't work the way I think it should or I've critically misinterpreted something. I'm pretty sure that the program is misleading at first glance to newbies like me because the "zero frequency" is actually a pole around 50 kHz and not where you tell it that that frequency should have zero gain (?). I've tried a bunch of things only to get errors or very mangled/destroyed waveforms. I know a pretty good deal about a lot of 78 RPM restoration but not so much about Nyquist. Hopefully this is possible. Thanks!

Now that I think about it, maybe it would work if I told it to implement a gain of around -20 dB? I want to be sure to make as few gain changes as possible and have it be the exact same thing as if i transferred the record with no RIAA emphasis/deemphasis in the first place. Expert opinions needed.

http://waynestegall.com/audio/riaaiir.htm
 
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I never implemented filters in Audacity, but if you are interested in digital RIAA correction, I can recommend Scott Wurcer's article in Linear Audio volume 10. By swapping the poles and the zeros/the denominators and the numerators, you can turn his RIAA filters into anti-RIAA filters.
 
Thanks, I'll check that out if I start running dry on options. This is a very unconventional application. I have a flat preamp, but I'm implementing a displacement-sensitive cartridge that has a natural RIAA curve. Most people want reverse RIAA curves to test cartridges. This needs to take a line-level input and emphasize the treble 20 dB at 20kHz and minus 20 at 0 dB.

I've tried to make a reverse RIAA curve in a digital application (CEDAR Cambridge's Precision EQ) manually, but it doesn't allow for accurate results.
 
The cartridge is designed to play modern LPs, so it has circuitry in the preamp to compensate for the constant velocity parts of the curve. It also has swappable stylii allowing for use of a full set of coarse-groove stylii, so it has some untested potential for unsurpassed-quality transfers of pre-RIAA material. While the frequency response is a little more fuzzy than a conventional cartridge, the time-domain response could be much better, especially compared to the moving magnet cartridges that are typically used to transfers 78s. There is virtually no mass to move, so it should trace the groove much better.
 
I've also read that FIR filters are functionally the same as IIR filters and that you can't hear the phase inaccuracies of FIR filters, but I'd rather not take that chance on preservation-grade transfers and restorations.
The correction filters used during recording are always minimum phase and your cartridge is very probably also minimum phase. You then need minimum phase correction filters to get a good overall phase response.

IIR filters are usually minimum phase, although you can design them to be non-minimum phase if you really want to. You can give FIR filters pretty much any phase response that fits in their length, linear phase, minimum phase, maximum phase, anything in between.

Minimum-phase FIR and minimum-phase IIR filters should work fine for your application, the others lead to unnecessary phase errors.
 
The cartridge is designed to play modern LPs, so it has circuitry in the preamp to compensate for the constant velocity parts of the curve. It also has swappable stylii allowing for use of a full set of coarse-groove stylii, so it has some untested potential for unsurpassed-quality transfers of pre-RIAA material. While the frequency response is a little more fuzzy than a conventional cartridge, the time-domain response could be much better, especially compared to the moving magnet cartridges that are typically used to transfers 78s. There is virtually no mass to move, so it should trace the groove much better.
I see, that sounds logical.
 
In further research today, I realized that Diamond Cut software has what I need, although I'm not entirely sure their IIR inverse RIAA implementation, while very clean, is as clean as it could be. The maximum deviation is -0.33 dB at 28 Hz. Not sure if my above-proposed solution would improve on that if I can get the math correct or if anyone's implemented anything more accurate in the last several years.

Good articles on the subject are, "Phase Equalization and its Importance in the Reproduction of Disc Records" by Gary Galo in the 2010 ARSC Journal
and
Digital vs. Analog Equalization of Disc Record Playback by Ron Tipton in the 2012 ARSC Journal.

I'd post them, but they're copyrighted material.
 
milwaukeeshellac, if I understood correctly, your cartridge + preamp combination is suitable for playing records recorded with RIAA curve, right?

Which curve should be used for those 78rpm disks? Unless they were cut with flat curve, you don't need inverse RIAA correction. Instead you need a compensation that will just fill the gap between RIAA and that particular curve. Usually, it's only few dB difference.
 
milwaukeeshellac, if I understood correctly, your cartridge + preamp combination is suitable for playing records recorded with RIAA curve, right?

Which curve should be used for those 78rpm disks? Unless they were cut with flat curve, you don't need inverse RIAA correction. Instead you need a compensation that will just fill the gap between RIAA and that particular curve. Usually, it's only few dB difference.
The inverse RIAA is for the "alternative setup" with the displacement-sensitive cartridge with a mandatory RIAA preamp. My primary setup is a conventional cartridge with a robust archival preamp with multitudes of period-correct analog curves.

Most of what I work with is 1920s jazz. Many of those are truly flat. Others are 250 turnover and -5 rolloff at 10kHz or 500 bass/ flat treble. I'd very much like to run some sort of compensation curve rather than reverse RIAA and then add the correct curves back in, but that's extremely tricky to do accurately. I've been feverishly researching this exact topic, but I can't find hard data on more then a couple points for each curve. Nobody, for example, seems to know where a -5 curve begins its transition from 0 dB. We just know that at 6800 Hz it's -3db. I think with slope difference issues it's basically impossible to replicate this with one curve in conventional software and it's a mathematical question far beyond my self-taught skill level.
 
Nobody, for example, seems to know where a -5 curve begins its transition from 0 dB. We just know that at 6800 Hz it's -3db. I think with slope difference issues it's basically impossible to replicate this with one curve in conventional software and it's a mathematical question far beyond my self-taught skill level.
Assuming you mean a first-order low-pass filter with 0 dB of DC gain and 5 dB of attenuation at 10 kHz:

It is below 0 dB at any non-zero frequency. Its gain is

-10 dB*log10(1 + (f/fc)2)

with fc ~= 6800.553621 Hz. At fc, the response is at -10 dB*log10(2) = -3.010299... dB.

If you mean -5 dB with respect to 1 kHz, then this equation is wrong. ejp did some calculations for that case recently.
 
Correct. I guess based on that, the 0 dB point would be 3400 Hz(?) edit- never mind, wrong... My math is rusty and I just plugged that into an online algebra calculator.

Is there a corresponding formula for bass turnover frequency (ignoring RIAA)? I need to solve for the point where a 250 Hz bass turnover curve is at 0 dB so that I can fine-tune my digital curves. The graph on the Audacity website seems to suggest that the 500 Hz bass turnover curve is 0 dB at somewhere around 2kHz.
 
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