eXCELLENT BREAKDOWNS OF FILTERS in simple, easy to understand terms as they pertain to dsd

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. However, the way they're commonly used and their resulting effects can be quite different.

Moving Average Filter:
In a moving average filter, you average the past 'N' samples to get the current output. It's like looking back over the last few seconds to see how fast you've been running on average. This kind of filter smooths out sudden jumps in the signal and is often used for noise reduction or signal smoothing.

Cascaded Comb Filter:

A cascaded comb filter, on the other hand, takes the current sample and adds to it a delayed version of itself, possibly scaling it by a factor. When you cascade multiple of these comb filters together, the effect becomes more complex, but the basic operation is similar: current sample plus delayed sample.

How They Relate:
Imagine you're checking the temperature every day. A moving average filter would be like saying, "The average temperature over the past week is 'X' degrees." This gives you a smoothed-out view of what the temperature has been like.
A (single) comb filter would be like saying, "Today's 'feels-like' temperature is a combination of today's actual temperature and the temperature from a week ago." A cascaded comb filter would then involve multiple such 'feels-like' calculations based on temperatures from various past days, leading to a more complex profile.
Now, if you set up a cascaded comb filter in a certain way, it can act similarly to a moving average filter. But they are usually employed for different purposes: moving average filters for smoothing, and comb filters for adding echo, reverb, or other time-domain effects.
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So, while you can view a cascaded comb filter as a specialized type of moving average filter, in practice they are generally used for different tasks.


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Andrew's comments on the above

The Cascaded Comb filter, a special case of moving average filter, is the type of filter used to filter DSD in native DSD DACs.  Multiple streams of the original 1-bit DSD stream are 'cascaded' upon each other, delayed by a sample.  

The Signalyst DSC Native DSD DAC has 32 of the 1-bit DSD streams cascaded on one another, offset by a single sample each.  This is a 33 level unary/thermometer coded FILTER/DAC.  Burr-Brown Native DSD chips like those in iFi products do something very similar, the difference I wish to highlight here is the amount of levels... there are only 8 cascaded/delayed streams, meaning a 9 level unary/thermometer coded FILTER/DAC.  Finally, I will mention T+A, the outstanding high end audio hardware producer out of Germany.  I can only repeat what I was told by one of their representatives, but their Cascade Comb filter has only 4 offset DSD streams, for a 5 level unary/thermometer coded FILTER/DAC.  

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. )