Rowetel

Following on from the subset vector quantiser [1] I’ve been working on improving speech quality in the presence of bit errors without the use of Forward Error Correction (FEC). I’ve tried two techniques:

1. Optimisation of VQ indexes [2][3]
2. Trellis based maximum likelihood decoding of a sequence of VQ indexes [4]

Digital speech and FEC isn’t a great mix. Speech codecs often work fine with a few percent BER, which is unheard of for data applications that need zero bit errors. This is because humans can extract intelligible information from payload speech data with errors. On the channels of interest we like to play at low SNRs and high BERs (around 10%). However not many FEC codes work at 10% BER, and the ones that do require large block sizes, introducing latency which is problematic for Push To Talk (PTT) speech. So I’m interested in exploring alternatives to FEC that allow gradual degradation of speech in channels with high bit error rates.

Vector Quantisation

Here is a plot that shows a 2 dimensional Vector Quantiser (VQ) in action. The cloud of small dots is the source data we wish to encode. Each dot represents 2 source data samples, plotted for convenience on a 2D plot. The circles are the VQ entries, which are trained to approximate the source data. We arrange the VQ entries in a table, each with a unique index. To encode a source data pair, we find the nearest VQ pair, and send the index of that VQ entry over the channel. At the decoder, we reconstruct the pair using a simple table look up.

When we get a bit error in that index, we tend to jump to some random VQ entry, which can introduce a large error in the decoded pair. Index optimisation re-arranges the VQ indexes so a bit error in the received index will result in jumping to a nearby VQ entry, minimising the effect of the error. This is shown by the straight lines in the plot above. Each line shows the decoded VQ value for a single bit error. They aren’t super close (the nearest neighbours), as I guess it’s hard to simultaneously optimise all VQ entries for all single bit errors.

For my experiments I used a 16-th order VQ, so instead of two pairs there were 16 samples encoded for each VQ entry. These 16 samples represent the speech spectrum. Hard to plot a 16 dimensional value but the same ideas apply. We can optimise the VQ indexes so that a single bit error will lead to a decoded value “close” to the desired value. This gives us some robustness to bit errors for free. Unlike Forward Error Correction, no additional bits need to be sent. Also unlike FEC – the errors aren’t corrected – just masked to a certain extent (the decoded speech sounds a bit better).

The Trellis system is described in detail in [4]. This looks at a sequence of received VQ indexes, and the trajectory they take on the figure above. It makes the assumption that the speech signal changes fairly slowly in time, so the trajectory we trace on the figure above tends to be small jumps across the VQ “space”. A large jump means a possible bit error. Simultaneously, we look at the likelihood of receiving each vector index. In a noisy channel, we are more sure of some bits, and less sure of others. These are all arranged on a 2D “trellis” which we search to find the most likely path. This tends to work quite well when the vectors are sampled at a high rate (10 or 20ms), less so when we sample them less often (say 40ms).

The details of the two algorithms tested are in the GitHub PRs [5][6].

Results

This plot compares a few methods. The x axis is normalised SNR, and the y-axis spectral distortion. Results were an average of 30 seconds of speech on an AWGN channel.

1. No errors (blue, bottom), is the basic VQ quantiser with no channel errors. Compared to the input samples, it has an average distortion of 3dB. That gets you rough but usable “communications quality” speech.
2. Vanilla AWGN (green) is the spectral distortion as we lower the Eb/No (SNR), and bit errors gradually creep in. FreeDV 700C [8] uses no FEC so would respond like this to bit errors.
3. The red curve is similar to FreeDV 700D/E – we are using a rate 0.5 LDPC code to protect the speech data. This works well until it doesn’t – you hit a threshold in SNR and the code falls over, introducing more errors than it corrects.
4. The upper blue curve is the index optimised VQ (using the binary switch algorithm). This works pretty well (compare to green) and zero cost – we’ve just shuffled a few indexes in the VQ table.
5. Black is when we combine the FEC with index optimisation. Even better at high Eb/No, and the “knee” where the FEC falls over is much less obvious than “red”.
6. Cyan is the Trellis decoder, quite a good result at low Eb/No, but a “long tail” – it makes a few mistakes even at high Eb/No.

Here are some speech samples showing the index optimisation and trellis routines in action. They were generated at an Eb/No = 1dB (6% BER) operating point on the plot above. The Codec 2 700C mode is provided as a control. In these tests of spectral distortion the 700C mode uses 22 bits/frame at a 40ms frame rate, the “600” mode just 12 bits/frame at a 30ms frame rate. I’ve just applied the index optimisation and trellis decoding to the 600 mode.

Mode	BER	VQ	Decoder	Sample1	Sample2	Sample3
700C	0.00	Orig	Normal	Listen	Listen	Listen
700C	0.06	Orig	Normal	Listen	Listen	Listen
600	0.00	Orig	Normal	Listen	Listen	Listen
600	0.06	Orig	Normal	Listen	Listen	Listen
600	0.06	Opt	Normal	Listen	Listen	Listen
600	0.06	Opt	Trellis	Listen	Listen	Listen

The index optimisation seems effective, especially on samples 1 and 2. The improvements are less noticeable on the longer sample3, although the longer sample makes it harder to do a quick A/B test. The Trellis scheme is even better at reducing the pops and clicks, but I feel on sample1 at least it tends to “smooth” the speech, so it becomes a little less intelligible.

Discussion

In this experiment I compared the spectral distortion of two non-redundant techniques to FEC based protection on a Spectral Distortion versus Eb/No scale.

While experimenting with this work I found an interesting trade off between update rate and error protection. With a higher update rate, we notice errors less. Unfortunately this increased the bit rate too.

The non-FEC techniques have a gradual “fuzzy” degradation versus a knee. This is quite useful for digital speech systems, e.g. at the bottom of a fade we might get “readability 3” speech, that bounce back up to “readability 5” after the fade. The ear will put it all back together using “Brain FEC”. With FEC based schemes you get readability 5 – R2D2 noises in the fade – then readability 5.

So non-FEC schemes have some potential to lower the “minimum SNR” the voice link can handle.

It’s clear that index optimisation does help intelligibility, with or without FEC.

At low Eb/No, the PER is 50%! So every 2nd 12-bit vector index has at least 1 bit error, and yet we are getting (readability 3 – readable with difficulty) speech. However the rule of thumb I have developed experimentally still applies – you still need PER=0.1/BER=0.01 for “readability 5” speech.

There are some use cases where not using FEC might be useful. A rate 0.5 FEC system requires twice the RF bandwidth, and modem synchronisation is harder as each symbol has half the energy. It introduces latency as the FEC codewords for a decent code are larger than the vocoder frame size. When you lose a FEC codeword, you tend to lose a large chunk of speech. Frame sync is slower, as it happens at the FEC codeword rate, making recovery after a deep fade or PTT sync slower. So having a non-FEC alternative in our toolkit for low SNR digital speech is useful.

On a personal note I quite enjoyed this project. It was tractable, and I managed to get results in a reasonable amount of time without falling down too many R&D rabbit holes. It was also fun and rewarding to come to grips with at least some of the math in [3]. I am quite pleased that (after the usual fight with the concept of coding gain) I managed to reconcile FEC and non-FEC results on a single plot that roughly compares to the perceptual quality of speech.

Ideas for further work:

1. Test across a larger number of samples to get a better feel for the effectiveness of these algorithms.
2. The index optimisation could be applied to Codec 2 700C (and hence FreeDV 700C/D/E). This would however break compatibility.
3. More work with the trellis scheme might be useful. In a general sense, this is a model that takes into account various probabilities, e.g. how likely is it that we received a certain codeword? We could also include source probability information – e.g. for a certain speaker (or globally across all speakers) some vectors will be more likely than others. The probability tables could be updated in real time, as when the channel is not faded, we can trust that each index is probably correct.
4. The “600” mode above is a prototype Codec 2 mode based on this work and [1]. We could develop that into a real world Codec 2/FreeDV mode and see how it goes over the air.
5. The new crop of Neural Net vocoders use the same parameter set and VQ, so index optimisation/FEC trade offs may also be useful there (they may do this already). For example we could run FreeDV 2020 without any FEC, freeing up RF bandwidth for more pilot symbols so it handles HF channels better.

Reading Further

[1] Subset Vector Quantiser
[2] Codec 2 at 450 bit/s
[3] Pseudo-Gray coding, K. Zeger; A. Gersho, 1990
[4] Trellis Decoding for Codec 2
[5] PR – Vector Quantiser Index Optimisation
[6] PR – Trellis decoding of VQ
[7] RST Scale
[8] FreeDV Technology

I’ve returned to speech coding after a year of playing with VHF and HF modems. This is somewhat daunting for me, as speech coding is R&D, which tends to be very open ended; it’s possible to work for months with no clear outcomes. In contrast the modem work is straight forward engineering, and I get the positive feedback of “having stuff work” on a regular basis.

So I’m trying to time box the speech coding projects to a few days work each. This is quite a personal challenge, as there are just so many variables and paths to follow. It’s so easy to go off on a tangent and watch the months pass!

In this particular project I’m looking at the Codec 2 700C Vector Quantiser (VQ), and exploring ways to make it more inherently robust to high pass and low pass filtering at the edges of the spectrum. The broad goal is to improve speech quality at a given bit rate, or support a lower bit rate at the same speech quality. I’m targeting bit rates in the 600 bit/s range, and the lower end of the quality range (communications quality speech).

Subset Vector Quantiser

It’s well known that the most important speech information is between 300 and 3000 Hz. Energy outside that range makes the speech sounds nicer, but doesn’t help intelligibility much. Analog modes such as SSB exploit this by band limiting the speech so that the transmitter power is used just to punch through information in the narrow bandwidth that matters.

With digital speech the RF bandwidth is not directly linked to the bandwidth of the decoded speech. For example FreeDV 700D uses around 1100 Hz of RF bandwidth, but the decoded speech has energy covering most of the 0 to 4000 Hz range.

Codec 2 encodes and transmits the speech spectrum on a regular basis. As well as encoding parts of the spectrum necessary for intelligibility, it also has to encode other features, such as the high pass and low pass roll off the microphone and analog filters in the sound card. These features don’t carry any intelligibility, but bits are consumed to encode them. When you have just 28 bits/frame – every bit matters!

Turns out that some of the wilder variations in the speech spectrum from different sources of speech are in the 0-300Hz and 3000-4000Hz regions, for example different high pass or low pass filtering for a particular microphone or sound card. This can upset the Codec 2 quantiser, e.g. it might expend bits modelling a particular low pass filter response – lowering the quality of the perceptually important 300-3000 Hz information.

So I’ve prototyped a Vector Quantiser (VQ) that just uses the information in the 300-3000 Hz range to quantise the speech spectrum. However the VQ is trained on the full range, so it uses that full range to synthesise the speech, hopefully recovering some of the extended spectrum. There is also a limiter before the VQ to reduce the dynamic range of the frames.

Here are some samples processed with the newamp1 two stage VQ, and the new subset VQ. Like the newamp1 algorithm, it works on vectors of K=20 mel-spaced magnitude samples. The speech codec is only partially quantised (10ms frames, original phase, unquantised pitch), so it would sound worse in a real world fully quantised codec. The “newamp1” algorithm is used for Codec 2 700C [1] (and employed in FreeDV 700C/D/E), and uses 22 bit/frame (550 bits/s at a 40ms frame rate). The subset VQ uses just 12 bits frame (300 bits/s at a 40ms frame rate).

Filename	newamp1	subset
big dog	Listen	Listen
cap	Listen	Listen
fish	Listen	Listen
hts2a	Listen	Listen

There are some samples where newamp1 sounds louder – this could be due to the gain limiter stage in the subset algorithm constraining the dynamic range. There also seems to be more high frequency response with newamp1, indicating subset is not recovering the high frequency speech energy as I had hoped. Both are quite intelligible, and acceptable for communications quality speech.

This table presents the mean square spectral distortion in dB*dB:

Filename	newamp1	subset
big dog	6.05	8.56
cap	9.03	8.10
fish	10.81	7.31
hts2a	10.51	8.62

Both the samples and objective results show the subset VQ is holding up OK next to the reference newamp1, despite the low bit rate. I’ve found that around 9 dB*dB spectral distortion gives acceptable results for my (low communications quality) use case.

I tried adding an artificial low pass filter above 3400 Hz to a couple of the input samples, to simulate what might happen from different microphones.

It seems to work OK with the low pass filtered input samples, they sound pretty similar to the sample using the original source (one of the goals of this work):

Filename	subset	subset low pass
cap	Listen	Listen
fish	Listen	Listen

Conclusions and Further work

I’m surprised that a single stage VQ is working quite well at just 12 bits/frame. It’s also encoding both the average frame energy and the spectral shape (I use a separate scalar quantiser for frame energy in newamp1). This is quite optimal from a VQ theory point of view, but sometimes not possible due to practical concerns such as the storage/CPU requirements for a single stage VQ.

Further work ideas:

1. Try a few more samples, and push this work through to a fully quantised speech codec.
2. Seeing it’s doing well with a single stage, it would interesting to see if it sounds better with multiple stages.
3. A single stage VQ enables other tricks, like non-FEC techniques to make the VQ robust to bit errors, such as sorting the VQ indexes [2] or Neural Net style training with bit errors.
4. Try different companding curves instead of the hard limiter, to better represent louder signals.

Links

[1] Codec 2 700C
[2] Codec 2 at 450 bits/s. Another single VQ Codec 2 mode, that can generate high frequency information using a similar approach to this post.
[3] Codec 2 700C Equaliser Part 2. A previous approach to handle a similar problem, in this case the speech is equalised before hitting a full band VQ.
[4] The script train_sub_quant.sh in This GitHub PR is used to perform the experiments documented in this post.

FreeDV 700D [9] is built around an OFDM modem [6] and powerful LDPC codes, and was released in mid 2018. Since then our real world experience has shown that it struggles with fast fading channels. Much to my surprise, the earlier FreeDV 700C mode actually works better on fast fading channels. This is surprising as 700C doesn’t have any FEC, but instead uses a simple transmit diversity scheme – the signal is sent twice at two different frequencies.

So I decided to develop a new FreeDV 700E waveform [8] with the following features:

1. The ability to handle fast fading through an increased pilot symbol rate, but also with FEC which is useful for static crashes, interference, and mopping up random bit errors.
2. Uses a shorter frame (80ms), rather than the 160ms frame of 700D. This will reduce latency and makes sync faster.
3. The faster pilot symbol rate will mean 700E can handle frequency offsets better, as well as fast fading.
4. Increasing the cyclic prefix from 2 to 6ms, allowing the modem to handle up to 6ms of multipath delay spread.
5. A wider RF bandwidth than 700D, which can help mitigate frequency selective fading. If one part of the spectrum is notched out, we can use FEC to recover data from other parts of the spectrum. On the flip side, narrower signals are more robust to some interference, and use less spectrum.
6. Compression of the OFDM waveform, to increase the average power (and hence received SNR) for a given peak power.
7. Trade off low SNR performance for fast fading channel performance. A higher pilot symbol rate and longer cyclic prefix mean less energy is available for data symbols, so low SNR performance won’t be as good as 700D.
8. It uses the same Codec 2 700C voice codec, so speech quality will be the same as 700C and D when SNR is high.

Over the course of 2020, we’ve refactored the OFDM modem and FreeDV API to make implementing new modem waveforms much easier. This really helped – I designed, simulated, and released the FreeDV 700E mode in just one week of part time work. It’s already being used all over the world in the development version of FreeDV 1.5.0.

My bench tests indicate 700C/D/E are equivalent on moderate fading channels (1Hz Doppler/2ms spread). As the fading speeds up to 2Hz 700D falls over, but 700C/E perform well. On very fast fading (4Hz/4ms) 700E does better as 700C stops working. 700D works better at lower SNRs on slow fading channels (1Hz Doppler/2ms and slower).

The second innovation is compression of the 700C/D/E waveforms, to increase average power significantly (around 6dB from FreeDV 1.4.3). Please be careful adjusting the Tx drive and especially enabling the Tools – Options – Clipping. It can drive your PA quite hard. I have managed 40W RMS out of my 75W PEP transmitter. Make sure your transmitter can handle long periods of high average power.

I’ve also been testing against compressed SSB, which is pretty hard to beat as it’s so robust to fading. However 700E is hanging on quite well with fast fading, and unlike SSB becomes noise free as the SNR increases. At the same equivalent peak power – 700D is doing well when compressed SSB is -5dB SNR and rather hard on the ears.

SSB Compression

To make an “apples to apples” comparison between FreeDV to SSB at low SNRs I need SSB compressor software than I can run on the (virtual) bench. So I’ve developed a speech compressor using some online wisdom [1][2]. Turns out the “Hilbert Clipper” in [2] is very similar to how I am compressing my OFDM signals to improve their PAPR. This appeals to me – using the same compression algorithm on SSB and FreeDV.

The Hilbert transformer takes the “real” speech signal and converts it to a “complex” signal. It’s the same signal, but now it’s represented by in phase and quadrature signals, or alternatively a vector spinning around the origin. Turns out you can do a much better job at compression by limiting the magnitude of that vector, than by clipping the input speech signal. Any clipping tends to spread the signal in frequency, so we have a SSB filter at the output to limit the bandwidth. Good compressors can get down to about 6dB PAPR for SSB, mine is not too shabby at 7-8dB.

It certainly makes a difference to noisy speech, as you can see in this plot (in low SNR channel), and the samples below:

Compression	SNR	Sample
Off	High	Listen
On	High	Listen
Off	Low	Listen
On	Low	Listen

FreeDV Performance

Here are some simulated samples. They are all normalised to the same peak power, and all waveforms (SSB and FreeDV) are compressed. The noise power N is in dB but there is some arbitrary scaling (for historical reasons). A more negative N means less noise. For a given noise power N, the SNRs vary as different waveforms have different peak to average power ratio. I’m adopting the convention of comparing signals at the same (Peak Power)/(Noise Power) ratio. This matches real world transmitters – we need to do the best we can with a given PEP (peak power). So the idea below is to compare samples at the same noise power N, and channel type, as peak power is known to be constant. An AWGN channel is just plain noise, MPP is 1Hz Doppler, 2ms delay spread; and MPD is 2Hz Doppler, 4ms delay spread.

Test	Mode	Channel	N	SNR	Sample
1	SSB	AWGN	-12.5	-5	Listen
	700D	AWGN	-12.5	-1.8	Listen
2	SSB	MPP	-17.0	0	Listen
	700E	MPP	-17.0	3	Listen
3	SSB	MPD	-23.0	8	Listen
	700E	MPD	-23.0	9	Listen

Here’s a sample of the simulated off air 700E modem signal 700E at 8dB SNR in a MPP channel. It actually works up to 4 Hz Doppler and 6ms delay spread. Which sounds likes a UFO landing.

Comments:

1. With digital when your in a fade, you’re a fade! You lose that chunk of speech. A short FEC code (less than twice fade duration) isn’t going to help you much. We can’t extend the code length because latency (this is PTT speech). Sigh.
2. This explain why 700C (with no FEC) does so well – we lose speech during deep fades (where FEC breaks anyway) but it “hangs on” as the Doppler whirls around and sounds fine in the “anti-fades”. The voice codec is robust to a few % BER all by itself which helps.
3. Analog SSB is nearly impervious to fading, no matter how fast. It’s taken a lot of work to develop modems that “hang on” in fast fading channels.
4. Analog SSB degrades slowly with decreasing SNR, but also improves slowly with increasing SNR. It’s still noisy at high SNRs. DSP noise reduction can help.

Lets take a look at the effect of compression. Here is a screen shot from my spectrum analyser in zero-span mode. It’s displaying power against time from my FT-817 being driven by two waveforms. Yellow is the previous, uncompressed 700D waveform, purple is the latest 700D with compression. You can really get a feel for how much higher the average power is. On my radio I jumped from 5-10W RMS to 40WRMS.

Jose’s demo

Jose, LU5DKI sent me a wave file sample of him “walking through the modes” over a 12,500km path between Argentina and New Zealand. The SSB is at the 2:30 mark:

This example shows how well 700E can handle fast fading over a path that includes Antartica:

A few caveats:

• Jose’s TK-80 radio is 40 years old and doesn’t have any compression available for SSB.
• FreeDV attenuates the “pass through” off air radio noise by about 6dB, so the level of the SSB will be lower than the FreeDV audio. However that might be a good idea with all that noise.
• Some noise reduction DSP might help, although it tends to fall over at low SNRs. I don’t have a convenient command line tool for that. If you do – here is Jose’s sample. Please share the output with us.

I’m interested in objective comparisons of FreeDV and SSB using off air samples. I’m rather less interested in subjective opinions. Show me the samples …….

Conclusions and Further Work

I’m pleased with our recent modem waveform development and especially the compression. It’s also good fun to develop new waveforms and getting easier as the FreeDV API software matures. We’re getting pretty good performance over a range of channels now. Learning how to make modems for digital voice play nicely over HF channels. I feel our SSB versus FreeDV comparisons are maturing too.

The main limitation is the Codec 2 700C vocoder – while usable in practice it’s not exactly HiFi. Unfortunately speech coding is hard – much harder than modems. More R&D than engineering, which means a lot more effort – with no guarantee of a useful result. Anyhoo, lets see if I can make some progress on speech quality at low SNRs in 2021!

Links

[1] Compression – good introduction from AB4OJ.
[2] DSP Speech Processor Experimentation 2012-2020 – Sophisticated speech processor.
[3] Playing with PAPR – my initial simulations from earlier in 2020.
[4] Jim Ahlstrom N2ADR has done some fine work on FreeDV filter C code – very useful once again for this project. Thanks Jim!
[5] Modems for HF Digital Voice Part 1 and Part 2 – gentle introduction in to modems for HF.
[6] Steve Ports an OFDM modem from Octave to C – the OFDM modem Steve and I built – it keeps getting better!
[7] FreeDV 700E uses one of Bill’s fine LDPC codes.
[8] Modem waveform design spreadsheet.
[9] FreeDV 700D Released

Command Lines

Writing these down so I can cut and paste them to repeat these tests in the future….

Typical FreeDV 700E simulation, wave file output:

./src/freedv_tx 700E ../raw/ve9qrp_10s.raw - --clip 1 | ./src/cohpsk_ch - - -23 --mpp --raw_dir ../raw --Fs 8000 | sox -t .s16 -r 8000 -c 1 - ~/drowe/blog/ve9qrp_10s_700e_23_mpd_rx.wav

Looking at the PDF (histogram) of signal magnitude is interesting. Lets generate some compressed FreeDV 700E:

./src/freedv_tx 700D ../raw/ve9qrp.raw - --clip 1 | ./src/cohpsk_ch - - -100  --Fs 8000 --complexout > ve9qrp_700d_clip1.iq16

Now take the complex valued output signal and plot the PDF and CDF the magnitude (and time domain and spectrum):

octave:1> s=load_raw("../build_linux/ve9qrp_700d_clip1.iq16"); s=s(1:2:end)+j*s(2:2:end); figure(1); plot(abs(s)); S=abs(fft(s)); figure(2): clf; plot(20*log10(S)); figure(3); clf; [hh nn] = hist(abs(s),25,1); cdf = empirical_cdf(1:max(abs(s)),abs(s)); plotyy(nn,hh,1:max(abs(s)),cdf);

This is after clipping, so 100% of the samples have a magnitude less than 16384. Also see [3].

When testing with real radios it’s useful to play a sine wave at the same PEP level as the modem signals under test. I could get 75WRMS (and PEP) out of my IC-7200 using this test (13.8VDC power supply):

./misc/mksine - 1000 160 16384 | aplay -f S16_LE

We can measure the PAPR of the sine wave with the cohpsk_ch tool:

./misc/mksine - 1000 10 | ./src/cohpsk_ch - /dev/null -100 --Fs 8000
ohpsk_ch: Fs: 8000 NodB: -100.00 foff: 0.00 Hz fading: 0 nhfdelay: 0 clip: 32767.00 ssbfilt: 1 complexout: 0
cohpsk_ch: SNR3k(dB):    85.23  C/No....:   120.00
cohpsk_ch: peak.....: 10597.72  RMS.....:  9993.49   CPAPR.....:  0.51 
cohpsk_ch: Nsamples.:    80000  clipped.:     0.00%  OutClipped:  0.00%

CPAPR = 0.5dB, should be 0dB, but I think there’s a transient as the Hilbert Transformer FIR filter memory fills up. Close enough.

By chaining cohpsk_ch together is various ways we can build a SSB compressor, and simulate the channel by injecting noise and fading:

./src/cohpsk_ch ../raw/ve9qrp_10s.raw - -100 --Fs 8000 | ./src/cohpsk_ch - - -100 --Fs 8000 --clip 16384 --gain 10 | ./src/cohpsk_ch - - -100 --Fs 8000 --clip 16384 | ./src/cohpsk_ch - - -17 --raw_dir ../raw --mpd --Fs 8000 --gain 0.8 | aplay -f S16_LE

cohpsk_ch: peak.....: 16371.51  RMS.....:  7128.40   CPAPR.....:  7.22

A PAPR of 7.2 dB is pretty good for a few hours work – the cools kids get around 6dB [1][2].