All the notch filters I saw were made on the presumption of tuning to the multiples of the sampling frequency, beacuse the images are centered on them. Unfortunately, that way they attack the noise mostly at the frequencies where it has the least energy and vice versa. It is true that the digital images are centered around the multiples of the sampling frequency, but at those frequencies, they have zero energy. That energy rises toward the left and right, and achieves the biggest level at the frequencies farthest (20kHz far) from those centers, and there they have significant levels. This fact is related to the first bad thing from the lists above. i.e. to the fact that the unfiltered sinewaves of frequencies under a few kHz look practically as good as they should. In other words, while images are nominally centered at 44.1kHz, 88.2kHz etc, at these frequencies there is actually nothing to be filtered, and there is a lot more to be filtered all around them. Practically, this means we might need notches at frequencies other than multiples of sampling frequency.

As said, the highest noise energy is at 44.1-20(kHz), 44.1+20(kHz), 88.2-20(kHz), 88.2+20(kHz), 132.3-20(kHz) etc, i.e. at 24.1kHz, 64.1kHz, 68.2kHz, 108.2, 112.3kHz etc, so we might need notch filters at 24,1kHz, 66.15kHz, 110.25kHz, 154.35kHz etc, instead. It is not necessary to use notches for images over 200kHz, because the simple first-order filter (possibly at some place other than that where notch filters are) could do this part of the work, without influence in the audio band just as a notch filter.

The first notch would be the special case. It should be centered at 24.1kHz or maybe a bit higher, but it requires special care to design it so as not to affect the audio band, especially not to affect the phase inside the audio band. When designed that way, however, it becomes too narrow to effectively cut images of any signals other than 20kHz. Also, this 24kHz notch introduces a notable amount of ringing into the square signal, so I'd rather avoid it.

Looking at the frontiers of such an approach to the filtering, i.e. in the balance between the effectiveness, linearity of the phase inside the audio band, the shape of the square signal, and simplicity of the signal path (yeah, nothing is literally at the signal path, but the loop is closing through all those paths), maybe it is the time to go back to some classic filter. One relatively low order filter with a relatively high Q has the additional bonus of giving the necessary peak to compensate for treble roll-off. Only one additional active stage is needed. Sounds simple and prosaic, but could do the job. Be it an active filter around the opamp or passive, with a buffer downstream. Maybe someone will find a way to implement an active filter around one simple source/cathode/emitter follower. The key for the implementation of the active filter, which gives us the opportunity to deal with resistors instead of the coils, is virtual zero output impedance. Otherwise, a resonant circuit formed by output impedance and feedback capacitor will occur.

I do not think that any filtering in itself will bring any improvement to sound. In fact, the opposite can happen. I am prone to believe the non-o/s needs a filter only if (the rest of) the system starts to distort audibly. It might be time to rethink the relationship between the ultrasonic hash and transient IMD. In the case of the Marantz CD63, one high-speed opamp (LM6172) applied after the unfiltered, 8fs oversampled delta/sigma DAC chip (SM5872) makes a miracle. Improvements in terms of clarity are huge. This DAC chip has a PWM output, like a class-D amplifier. Not really digital, but the waveform is square shaped. (For the mainstream (oversampled) commercial units, the analog filters are also obligatory. They remove a residue of the oversampling process, thus protecting the downstream components from the IMD and its varieties. In reality, these filters are built with the stuff that already produces such artifacts). Recently, I had a chance to listen to the system with the unfiltered non-o/s DAC as a front end, and some discs and some frequencies made it go crazy. At the same time, putting these ugly events aside, it sounded as clean as it should. This could be related to the content of the non-o/s noise - while its overall level is higher, it resides at lower frequencies.

So, the no_filter approach might not be the one-fits-all solution. But much more important than that is the fact that digital audio can work this way, and that is one of the best ways it can work at all. Filter definitely could be avoided by using decent amplifiers and solidly built tweeters, later possibly with frequency response not going above 20kHz. The bulk of good amplifiers and speakers will save you from thinking about the filter.

The merits and shortcomings of the particular filters mentioned above could be more clear by looking at the simulations I made using Linear Technology SwitcherCAD. The name of this program is associated with the one specialized for the simulations of the switching supplies, but it is a (free) fully working general spice program. It offers that great opportunity to simulate circuits with wav files at the input. As wav file, naturally, does not include sample and hold, observed waveforms for which FFTs are done are connect-the-dots derived. Speaking generally, this should be treated as an error. If you want to model the input better than I did, it is fine, but principally it will not change anything because the relation between square and triangle waves is quite simple, so the original FFT graphs scaling was easily corrected. In the FFT graphs without scaling on the Y axis one field should be considered as 10dB tall. Resistor 1k in all schematics is an I/V resistor that applies to TDA1543 and if it has some different value, the rest of the filter should be remodeled accordingly.


Pedja Rogic, April 2003