Oscillations in the impulse response of IIR filters arise due to pole placement in the z-plane. Poles with non-zero imaginary components cause sinusoidal oscillations, with those closer to the unit circle resulting in longer-lasting ringing. High-Q filters, narrow frequency bands, higher filter orders, and feedback loops can amplify these oscillations, while numerical errors in fixed-point implementations may destabilize the system by shifting poles.
The trade-offs involve balancing sharp frequency selectivity with increased ringing, maintaining stability while achieving high resolution, and reducing oscillations at the cost of computational complexity or filter order.
Will try to do some measurnments, once back at home.
Indeed the ripple percentage sets the steepness of cut off of the Chebyshev (IIR) filter . If you set the ripple to 0% you have a relatively slow cutoff there will be no ripple. This is the filter that Naim use, in this state its called a Butteworth filter - and this is one reason why the oversampling is applied to data. Ripple will occur with FIR and IIR
For anyone else following - and interested in DSP as used in audio (and elsewhere), a great text is The Scientist and Engineer’s Guide to Digital Signal Processing by Steven W. Smith, Ph.D - it was my go to text for DSP in recent years and is very accessible - for the above discussion Chapter 19 to 22. There is a free download of his book that the author provides - search in your favourite search engine
This is the impulse response of Atom at 44.1kHz with the new software. My plan was to purchase a second hand unit with old software and perform measurements before and after the new firmware update. Unfortunately the unit came with the updated software:) and was only able to compare it with nDAC, that exhibits the same oscillations, but it decays two times faster. Phase and SPL are nearly equal, no major deviations.
In my opinion the perception of brightness comes from the extended decay and oscillations of the impulse response.
Even if this firmware can be tweaked further if something in the SQ is really not as intended, to me it still and definitely sounds superb, and is an improvement in the spirit of what I liked about the NC and why I bought it. I hope Naim maintains this direction and signature overall. I know it’s hard to believe (especially if one is looking at the other thread where patience and positive feedback have been discouraged) but I may be speaking for the majority of people enjoying their music even more.
A true impulse or Dirac Delta function is of course an artificial abstraction… it’s impossible to create, it is a mathematical modelling tool. … in this context an impulse has zero time width… so typically one uses an impulse response approximation where the width of the time of the rectangular impulse is a lot smaller than the system response time.
They key thing with filters and certainly with audio filters is whether the ripple is in pass band, transition band or after the cutoff… and that is where different filters have different responses and dependent on the Q.
Below is the IIR reconstruction filter response of the NDAC, and the ripple in the pass band… these are copied from the Naim DAC white paper.
I understand the same filter has been used on all Naim streamers since.
Have to say I am absolutely loving this software release on my ndx2 feeding DAVE… it sounds so natural and clear with lovely extended non etched insight… timbres and balance to die for… the bass kick transients are deep and tight … and totally tuneful with nice sub bass… enjoying Mau P and Massano right now. I know this is using a separate high end DAC, and I have room bass trap treatment, but the SPDIF stream is key, and I can hear differences in firmware releases on the Naim streamer.
Using a frequency sweep and deconvolution method is scientifically valid and widely accepted in audio analysis. The impulse response derived reflects the actual behavior of the nDAC’s IIR filter, including the expected oscillations at 24 kHz, which result from its high Q near Nyquist frequency.
SPL that you kindly provided shows amplitude variation across frequencies, but it doesn’t provide temporal details like ringing or oscillations caused by high-Q filter designs.
Yes, unfortunately, a big step backwards. From a pleasant analogue sound with perfect timing to a hard and sharp sound. Which can only be listened to at very low volume.
It shows the small passband ripple (small hump before the cutoff) on the 48 kHz trace… I’m sure if Naim changed the scales you would see more of the ripple.
But I am talking about time domain, not frequency domain. Look at your book page 54 and page 338. Both Chebishev and Butterworth have ripples in the time domain, i.e. in your book the author examines the step response, where I measure the impulse response (but they are both in the time domain).
Ok - but I was referring to the frequency domain in my posts… so yes a time domain response against an impact response can show how that input is responded to by a filter by changing its shape over time, where as the frequency domain shows how the frequencies of that response are distributed.
I tend to consider frequency domain analysis is more useful for audio filters, because our ears-brain combination is a frequency domain analyser as it splits the the hear audio spectrum into narrow bands to determine power in each band.
If I was looking at control systems I might be more inclined to look at the time domain response.
But I guess we are kind of talking about apples and pears
If the nDAC is representative of the pre-FW update state, then filter parameters have changed. I believe this is what we are hearing, this slower decaying post-ringing.
This is also what I think has happened, however to validate it we need to test one and a same DAC before and after the firmware update. Fortunately I have one bullet left, the network streamer ND5XS2. It is still not updated.
