FIR Filter:

An FIR filter is like a simple sieve at the end of the slide. As the marbles roll down, the sieve lets only the blue marbles through.

1. Memory: This sieve doesn't remember any of the marbles that came before. Each marble is dealt with then and there, and the sieve forgets about it.
2. Stability: It's pretty stable; if a red marble sneaks through, it won't mess up your blue collection for long.
3. Precision: You can make the holes in your sieve very precise, but sometimes it takes a lot more effort (computation) to make a really good FIR sieve compared to an IIR sieve.

IIR Filter:

An IIR filter is like a smarter, but more complicated, sieve that remembers some of the previous marbles. It might let a blue marble through, then think, "Hmm, the last few marbles were blue, so I'll be a little more lenient with the next one."

1. Memory: This sieve remembers some of the marbles that came before and uses that memory to decide on letting future marbles through.
2. Stability: Because it remembers past marbles, if a red one sneaks through, it might affect the next few decisions it makes. It's usually stable but can be trickier to set up right.
3. Efficiency: It often takes less effort (computation) to make a good IIR sieve compared to an FIR sieve, especially for similar tasks.

Summary:

• FIR filters are like simple, forgetful sieves. They are stable and can be very precise, but sometimes they take more effort to set up.
• IIR filters are like smart, remembering sieves. They are usually more efficient but can be less stable and require more careful setup.

Both types of filters are used to process audio signals, either to enhance certain features or remove unwanted noise, much like how our marble sieves are used to sort the marbles.

DO IIR Filters have Delay Lines like FIR filters??

In digital signal processing, the term "delay line" is often associated with FIR (Finite Impulse Response) filters, where the filter uses a series of past and current samples to compute each output. Essentially, the delay line in an FIR filter holds onto past samples of the input signal, which are then used along with the current sample to calculate the output.

IIR (Infinite Impulse Response) filters, on the other hand, use not only past input samples but also past output samples to compute the current output. While they don't have a "delay line" in the same sense as FIR filters, they do have a form of memory that stores past values. This "memory" isn't typically referred to as a delay line, but it serves a similar purpose: it holds past information that the filter uses to calculate its output.
So, in simple terms:

• FIR filters have a delay line for storing past inputs.
• IIR filters don't have a "delay line" per se, but they do store both past inputs and past outputs to compute the current output.

Both kinds of filters can introduce some amount of delay to the signal, but the way they use past information is different. FIR filters rely solely on past and current input values, while IIR filters use both past input and past output values.

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What is a Cascade Comb type Integrator vs. a Moving Average Filter explained very simply?

Let's imagine you're trying to figure out how fast a group of people are running. You could use different methods like a Cascade Comb Type Integrator or a Moving Average Filter. Both aim to give you a general idea, but they work a little differently.

Moving Average Filter:
Think of this like taking a quick glance at your stopwatch every few seconds and averaging those speeds. This method will give you a pretty good idea of how fast people are running right now.

• Simple to Understand: It's like taking an average grade from your last three tests in school.
• Immediate: It's quick to tell you what you want to know, but might be a bit jittery if people speed up or slow down suddenly.

Cascade Comb Type Integrator:
Imagine instead you're using a more complex method where you don't just look at the most recent times but also consider times from way back, maybe even from when the race started. This would be like calculating your grade point average (GPA) throughout all your years in school, not just the recent tests.

• Complex: It considers a lot of history, so it's a bit more complicated than just averaging the last few times.
• Smooth but Delayed: This method might take a little longer to react to sudden changes because it's considering a long history.

In summary:

• A Moving Average Filter is like checking the speed every few seconds and averaging it. It’s quick and simple but reacts to sudden changes quickly, which might be good or bad depending on what you want.
• A Cascade Comb Type Integrator is like keeping track of speeds from the beginning of the race to now. It gives a more smoothed-out view but might be a bit slower to react to sudden changes.

Both have their pros and cons, and the right one to use depends on what exactly you want to know.

How are Comb Filters used in Audio Processing?  

In the context of audio signal processing, a Cascade Comb Type Integrator (often referred to simply as a "comb filter") is a filter used for various applications like reverb, echo, and other time-domain effects. It's different from a moving average filter and has its own characteristics.

How it works in audio:
A comb filter adds a delayed version of the signal to itself, creating peaks and troughs at regular frequency intervals (hence the name "comb"). When cascaded—or chained together—multiple comb filters can provide a more complex and tailored frequency response.

What does it do to the audio?

1. Reverb and Echo: One of the primary uses is to create reverb and echo effects. By adjusting the delay time and how the delayed signal is mixed with the original, you can create anything from small room reverb to large hall echoes.
2. Sound Coloring: Comb filters create a unique frequency response with regularly spaced peaks and troughs. This can be used to "color" the sound in a specific way.
3. Other Effects: In a cascade, the effect becomes more complex and versatile. By chaining multiple comb filters, you can create intricate reverbs, choruses, or other time-domain effects.

Simple Analogy:
Imagine you're in a hallway and you clap your hands. The sound of the clap will bounce off the walls and come back to you at different times, creating an echo or reverb effect. Each bounce is like a single comb filter. When you cascade them, it's as if you're in a more complex environment where the sound bounces off multiple surfaces at various distances, creating a more intricate echo or reverb effect.
So, in audio, a Cascade Comb Type Integrator (or cascaded comb filter) is often used for creating complex time-based effects like reverb or echo. It's different from a moving average filter, which is often used to smooth out a signal but doesn't create the time-based effects that a comb filter does.

How are these Cascade Comb Filters used in DSD Processing? 

Digital Stream Digital (DSD) is a high-resolution audio format that uses Pulse-Density Modulation (PDM) instead of the more commonly used Pulse-Code Modulation (PCM). In DSD, audio is represented by a series of 1s and 0s, where the density of 1s indicates the amplitude of the signal. It's a bit like morse code for audio; a bunch of 1s close together represent a high point in the audio wave, and a bunch of 0s represent a low point.
A Finite Impulse Response (FIR) comb filter can be used in DSD audio processing to achieve certain effects or improvements in sound quality.

FIR Comb Filter in Simple Terms:
Imagine you are jumping on a trampoline. Each time you bounce up, you touch a hanging bell, which rings. If you bounce higher, you can touch bells that are hanging further away. The first bell represents the immediate sound, and the bells hanging further away represent echoes or repetitions of that sound.

In a similar fashion, a comb filter creates a series of echoes or repetitions in your audio. An FIR comb filter does this by adding delayed versions of the original signal to itself.

Application in DSD:

1. Noise Shaping: DSD inherently has a noise floor that rises at higher frequencies. An FIR comb filter can help move or 'shape' this noise to frequencies that are less audible to human ears, thus improving audio quality.
2. Echo or Reverb: If you're using DSD for recording or playback, you might use an FIR comb filter to add a specific echo or reverb effect to the audio.
3. Sound Coloration: Sometimes you might want to add a unique character or "color" to the sound. Comb filters, by their nature, can alter the frequency response of the audio in such a way that it brings out or diminishes certain tonal qualities.
4. Decimation: When converting high-resolution DSD to a lower sample rate PCM, an FIR comb filter can help in preparing the signal for decimation by removing certain frequencies.

So in essence, an FIR comb filter in DSD can help in shaping the sound, either to improve quality or to add specific effects. It's like choosing which bells you want to ring as you jump on the trampoline, each creating a unique bounce pattern and sound.

But isn't is still true a Cascade Comb filter is a type of Moving Average Filter?

You're correct that a cascaded comb filter can be viewed as a specialized form of a moving average filter, particularly when it's implemented with Finite Impulse Response (FIR) characteristics. Both are linear filters, and both can be used to smooth out or otherwise modify a signal. 

Why do the call them 'comb' filters?  Because when viewed in FFT , they look like this... a bit like a comb.  (this is the S.M.S.L D300 native DSD filter output at DSD64, fc at 13khz. ) 

I named the S.M.S.L D300 DAC my current King of Budget Esoterica.  It sounds way, way better than just another one in a line of nice budget kit, as long as certain conditions are met.  Rather than re-hash all of that, I encourage you to click here and check my review if you have not already done so.  

The issue isn't with my ears.  I can hear just fine even as I approach 50 years.  Not that it helps with reviewing audio equipment, it can't hurt that I am a classically educated college level musician with perfect pitch.  It's nothing to me to notice overtones, also known as harmonics, both what should be natural to the music, and what is 'added' as harmonic distortion by the 'bad, bad' equipment.  I never have really understood the aversion to harmonic distortion.  It's, well, HARMONIC.  The first harmonic is the fundamental, the second harmonic is the Octave, which means its the exact same note just twice the frequency rate.  The 'mean old nasty' third harmonic?  Its a perfect fifth above the second harmonic, and therefore is also consonant with the fundamental.. they call it perfect for a reason.  Fourth harmonic?  Its a perfect fourth.  Which guess what?  Is the exact same note as the fundamental and the second harmonic!  The are all climbing in an octave sequence.  Yes, I get that equipment that adds or accentuates these things MAY not represent the musical performance accurately.  But I also 'get' that I LOVE the way music sounds on tube amplifiers.  I have NO technical or scientific argument or treatise to give you on what makes for the best musical reproduction.  All I know is I know what I like when I hear it.  It stands out from amongst all kinds of 'copy cats' in a saturated market.  

You know what else I like?  I am about to welcome you into the cognitive dissonance in which I daily live.  I like to know what my hardware is doing on the electronic level.  Measurements mean things to me.  Surprisingly, they are important.  I mean, we have to have SOME BASIC standards, right?   I think we passed those benchmarks a long time ago actually, and the crazy low noise and distortion stuff out there is way past our ear's resolution.   Yet no one is suddenly claiming digital audio is cured of all its 'digititis'.  No one, except maybe a few of that same old cult are proclaiming perfect audio.  Same guys who have been yelling 'bits are bits' since the CD hit the scene.  (Reminds me of an episode from back in the early 90's when a friend of mine insisted that CD was the thing of the past.. DAT was the real deal and the future... I will let you laugh and clear before we move on. )

So what is my problem??  I am obviously talking about the S.M.S.L D300 DAC.  Its PCM measurements are impeccable and it doesn't sound in any way clinical or digital; it frankly sounds amazing. 

The PROBLEM came when I started seeing the DSD measurements.  The DSD filters are very low, and very slow and gentle.  All good so far for the DSD crowd, like me, who wants gentle filters to maximize transient performance and minimize ringing.  DSD should be different than PCM.  Many DACs just make DSD as much like PCM as possible without actually saying that to the buying public in order to quietly deal with its major issue... all that ultrasonic noise.  Ummm... THAT is where we run into the problem with the S.M.S.L D300.   Something is off with the analog stage. 

The numbers not only are worse than their PCM equivalents, as we go up in oversampling speed, they get much worse.  Certain websites would be panning this thing with trophies that have missing parts. 

My best guess is the issue is in the secondary analog filter that should come after the initial FIR conversion filter.   For instance, iFi has their DSD FIR filter converter followed by a RC analog filter at 80khz to keep the DSD time domain superiority intact while dealing with the remaining ultrasonic noise in a way that adds no new ringing at all, and maintains the signal to noise ratio and harmonic distortion at levels that match its PCM performance.  Same with pretty much every other 'native' DSD DAC I have sitting around.  

But not this S.MS.L.  And damned if it defies the measurements and still sounds amazing anyway, especially at the 'sweet spot' I identified. 
​What would normally be sacrilege for a 'purist' like me, I caved and am oversampling everything to DSD256 and have chosen to set the filter at 104khz.  And it sounds GLORIOUS.  And it sounds about as good, as anything I have, including the RME ADI-2 PRO FS R BLACK EDITION in DSD Bypass mode, which not only sounds great, it measures the part.  The only native DSD kit I have that really kindof makes quick work of the S.M.S.L is my Signalyst DSC2 discrete DSD converter build, which ironically really doesn't measure that well either since it uses good ol' fashioned transformer outputs like the good ol' tube days.  

So with my rant over and my cognitive dissonance as active as ever, I will share with you what the DSD measurements from the S.M.S.L look like on paper.  These tests are done either with Multitone's internal modulator that converts all its test tones to DSD, or they are DSD tones tones made by HQPlayer played back via external sources.  ADC in use as always is the E1DA Cosmos, so we are in good technical hands here I assure you.  Allright.. on with the show.  

I thought you might like a look at some data charts pulled from my archives... We all love (or many of us just quite frankly hate) more charts and data!  I am starting to develop that love/hate relationship with it... leaning toward the 'hate' part, because every second I am taking measurements or preparing them for publishing is a second that I was at one time and could be at this time actually enjoying the hobby of LISTENING!   Maybe someday I can afford what those fancy shmancy sites have.. those people who do things for you for pay.  Alas, for now, it is me doing the measuring AND inputing the data. 

I came of age with computers as a teenager in the early to mid 1990's.  I have been there for it 'all'.  Well almost anyway.  From the days of 'Quantumlink' dialup on the Commodore 64, to the 'You've Got Mail!' sound every time I logged onto to America Online!  from my mid 1990's Macintosh Performa, all the way to the invention of the iPad, Smartphone, etc, and I still feel like a complete idiot around Gen Z who whiz around their smart technology like their smartphone was grown with them in the womb.  

That is a long way of saying, yeah, I am more computing challenged than I would like to admit, being a 'pioneer' and all that haha.  

Anyway.. all that rubbish said, here is an early preview of the measurements of the iFi iDSD PRO 4.4mm Pentconn output version.  Full review finally coming early next week.