# Talk:Digital filter

## Sketch of possible article structure

• Characterization
• Introduce the state-space form as well
• 2D and multidimensional filters
• Impulse response, step response, frequency response
• Linearity
• Time-invariance
• Causality
• Filter design
• Design of IIR
• Analog to digital transforms (bilinear, invariant impulse)
• Optimization techniques (i.e. using iterative techniques to design a filter to specifications)
• Design of FIR
• Window method
• Optimization techniques
• Discuss FIR vs IIR
• Realization
• Structures
• Implementation
• Emphasis on multiply-accumulate
• Fixed-point considerations
• Relationship to digital signal processing
• Time-varying filters
• Multi-rate filters
• Applications
• Audio
• Communications
• Control systems
• Astronomy
• Video
• Image processing —Preceding unsigned comment added by Dspetc (talkcontribs) 07:50, 9 October 2008 (UTC)

## Wrong name throughout

The name of this article should be discrete-time filter, and it should contrast with continuous-time filter. In both cases, the filters are "analog" because values at each time come form a continuum that is analogous to values seen in the physical world. What makes a filter "digital" is that its values are quantized; the word "digital" comes from the Latin for the digits of the fingers – if it can't be counted, it can't be digital. Quantization is only mentioned once in this article, and it's essentially a footnote. Either this article needs to be made specific to digital filters (e.g., deal with all of the issues with filter implementation on digital computers) or its name needs to be changed. Right now it's confusing at best and misleading at worst. —TedPavlic (talk/contrib/@) 23:49, 3 July 2009 (UTC)

Speaking for Ted's POV, and off-the-cuff, given that we commonly use digital filters to filter analog signals, it is important to remember that every such digital filter is preceded by a discrete-time analog filter (the S/H function), and is followed by another discrete-time analog filter (the reconstruction filter). Sometimes the time and space difference between the two functions are very large, as in digital audio recording (e.g., in the studio) and playback (e.g., on portable audio devices). There are also many examples (albeit increasingly historical) of discrete-time analog filter systems, all of which include the S/H and reconstruction filter functions previously mentioned. The formerly numerous National Semi switched capacitor filter chips come to mind. -Al Roxburgh 8-28-2013.

While you could make a case that discrete-time filter would be a better name, it seems over the top to call digital filter incorrect, since discrete-time filters have been commonly referred to as digital filters in thousands of books and papers since the 1960s, even when only discussing difference equations without quantization. Dicklyon (talk) 00:44, 4 July 2009 (UTC)
The word digital means that values must be quantized, and that's all it means. When a designer says "digital," the first question his boss asks involves the word "resolution." You can't have one without the other. Furthermore:
• A sample and hold device is an analog latch, and the combination of two of them triggered on different edges forms an analog flip flop. That analog flip flop is an analog sampler (i.e., discrete time) that takes samples from a continuum of values. This simple circuit has been used for decades to demodulate PWM signals, like the ones generated from example PWM modulation circuits shown on 555 timer IC datasheets. [1]:p. 8 Hence, discrete-time does not imply digital.
• A comparator (or, more generally, any flash ADC) can generate quantized versions of signals that exist over a continuum of time and, in fact, have jumps that come from a continuum of time. However, those jumps will come from a measure zero set (i.e., a countable number of values). So digital does imply discrete-time.
Consequently, it certainly is acceptable to take discrete time for granted when discussing "digital" filters. However, as shown in the sample and hold example, it's just wrong to assume that all discrete-time applications are digital. In fact, the Shannon–Nyquist theorem fails when a continuous-value signal is both sampled and quantized. The well-known Shannon–Nyquist sampling theorem requires that samples of the continuous signal are exact. So I argue that the references you mention are using digital/computer applications to justify the use of discrete-time. However, they purposely avoid the complicating topic of quantization; after all, even contemporary researchers have a poor understanding of even the spectral properties of quantizers. —TedPavlic (talk/contrib/@) 14:42, 4 July 2009 (UTC)
In the DSP field, most of what's studied, taught, and written about has nothing to do with the signals actually being quantized. Just as in numerical analysis and many other applications of digital computers, the fact that signals must be quantized is often completely ignored, hidden by the use of double-precision arithmetic and such, or left for a later phase of design when finite-word-length effects are considered. These considerations that you call "digital" are often only a small part, or missing completely, in works on digital filters. In writing wikipedia articles, it's important to represent things as they are, or as they are represented most commonly in sources, not as we would like to logically reconstruct them. Dicklyon (talk) 15:16, 4 July 2009 (UTC)
In my DSP texts (e.g., Mitra's well-known textbook on Digital Signal Processing), quantization is topic on which considerable text is devoted. In the laboratories I teach, students see the effects of quantization first-hand. For example, filters that were stable and/or had zero steady-state error in simulation chatter wildly in the laboratory (a great example for students having trouble understanding describing functions). In many cases, the trajectories of the laboratory systems follow strange trajectories that reach zero DSP error in finite time (which, itself, is fascinating) although in real life have possibly massive error. In my industry experience, the quantization noise floor is ever-present; this is the major reason why sigma-delta converters (and sliding mode control as well) are so hyped right now. It's true that introductory texts avoid the quantization topic, but quantization effects eventually have to be dealt with by any serious digital and mixed-signal engineer. —TedPavlic (talk/contrib/@) 12:19, 6 July 2009 (UTC)
Agreed. I don't think that conflicts with what I said above. Dicklyon (talk) 16:03, 6 July 2009 (UTC)
Despite the niggles, I think this is a really nicely-written introduction/explanation of what a digital filter is for the neophyte... I hope the article expands in the same style to satisfy the concerns of our demanding interlocutors! 87.113.14.239 (talk) 16:50, 16 August 2009 (UTC)User: macdaddy

## Simple edit to impulse response

I made a simple edit to try make the explanation of impulse response more clear. This mainly consisted of placing links to the Infinite impulse response and Finite impulse response pages, as well as putting simple explanations for the difference and the general form of the respective equations.Drunken Possum (talk) 21:37, 25 April 2010 (UTC)

## Question:

Is there an error on the Type 1 diagram? I believe -a0 should read +a0. —Preceding unsigned comment added by Heathera skidog (talkcontribs) 20:51, 28 May 2010 (UTC)