On Tue, 22 Feb 2005 00:54:54 -0800, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:> >"Allan Herriman" <allan.herriman.hates.spam@ctam.com.au.invalid> wrote in >message news:ehak119ie6q0tlp7k9gka22uub34mrtkvl@4ax.com... >> On Mon, 21 Feb 2005 10:14:44 -0800, "Fred Marshall" >> <fmarshallx@remove_the_x.acm.org> wrote: >> >>> >>>"Allan Herriman" <allan.herriman.hates.spam@ctam.com.au.invalid> wrote in >>>message news:dprj1198ics0h3co4tq6qs31h45vpo14q1@4ax.com... >>>> On Mon, 21 Feb 2005 14:08:08 GMT, Randy Yates <yates@ieee.org> wrote: >>>> >>>>>"huke" <hugo.harada@gmail.com> writes: >>>>> >>>>>> Hello Everyone, >>>>>> >>>>>> Can anyone point me the definition for a transversal equalizer? Some >>>>>> books only treat linear and adaptive equalizers, and some talk about >>>>>> transversal equalizers. It seems that all linear equalizer are >>>>>> transversal equalizers but I not convinced that this is true and I do >>>>>> not know if the opposite holds as well!? Very confused!! >>>>>> >>>>>> Pointers to references are also appreciated. >>>>>> >>>>>> Looking forward to hearing from you, >>>>>> >>>>>> Huke >>>>> >>>>>Hi Huke, >>>>> >>>>>Here is the way I would categorize these terms: Equalizers can be >>>>>either adaptive or fixed. Within either of those categories, you >>>>>can have the following subdivisions: >>>>> >>>>> linear non-linear >>>>> | >>>>> --------------------- >>>>> | | >>>>>transversal (FIR) non-transversal (IIR) >>>>> >>>>>See, e.g., Proakis' "Digital Communications" section "Linear >>>>>Equalization." >>>> >>>> >>>> Note that transversal implies FIR, but FIR does not imply transversal. >>> >>>Alan, >>> >>>Can you explain further? I don't see a difference. >>> >>>For example, both have FIR so I agree that transversal implies FIR. >>> >>>So, there must be something that you attribute to FIR that somehow makes >>>it >>>non-transversal. The application of coefficients is on samples or a >>>continuum (either one) that transeverses (goes across) time (or whatever >>>the >>>sample domain might be - such as space/distance). >>> >>>Whether the data is continuous or discrete samples doesn't change the >>>nature >>>of FIR. >>>But, I hasten to acknowledge that *most* of the time we refer colloquially >>>to "FIR" as a filter that operates on discrete (and quantized) samples. >> >> Hi Fred, >> >> I assume that 'transversal' is a property of a filter implementation, >> whereas 'FIR' is a property of the impulse response of a filter. >> >> I'm using your definition of transversal (from an earlier post in this >> thread), which I interpreted as meaning that the output would be >> formed by adding weighted time delayed copies of the input signal. >> >> To prove my point that FIR does not imply transversal, we need to find >> a filter that is both (1) FIR, and (2) not transversal. >> >> A boxcar averager (as used in a CIC) is an example of such a filter, >> as it has a recursive implementation. >> >> y[n] = y[n-1] + x[n] - x[n-k], for some constant k, and y[-1] = 0. >> >> This gives the same (finite) impulse response as this transversal >> filter: >> n >> y[n] = sum x[n] >> n-k+1 >> > >OK - if we include recursively implemented FIRs then they aren't >transversal. >But, that's a special case that only applies to a small subset of FIRs. >Correct but limited. I like to think of the recursive implementation of >FIRs as sort of a curiosity with limited application - no matter how cool >and even valuable some of those implementations may be. Let's not have the >tail wag the dog. > >What if we turn it around and say: >"In some cases a FIR can be implemented recursively and then isn't a >transversal filter. However, a FIR filter can *always* be implemented as a >sum of delayed inputs and thus, can always be transversal" ?? >In that sense, FIR can very reasonably imply transversal.They never should have stopped teaching logic in schools. Allan
Definition for transversal equalizers
Started by ●February 20, 2005
Reply by ●February 22, 20052005-02-22
Reply by ●February 22, 20052005-02-22
Fred Marshall wrote:> OK - if we include recursively implemented FIRs then they aren't > transversal. > But, that's a special case that only applies to a small subset of FIRs. > Correct but limited. I like to think of the recursive implementation of > FIRs as sort of a curiosity with limited application - no matter how cool > and even valuable some of those implementations may be. Let's not have the > tail wag the dog. > > What if we turn it around and say: > "In some cases a FIR can be implemented recursively and then isn't a > transversal filter. However, a FIR filter can *always* be implemented as a > sum of delayed inputs and thus, can always be transversal" ?? > In that sense, FIR can very reasonably imply transversal.I don't think that's good enough. (It's always better to write what one means.) Flat statements are rightly construed to include "always" by implication. Leaving out "usually" when we mean that usually leads to subsequent error. Example: "To avoid aliasing, a signal must be sampled at a rate at least twice its highest frequency." Counterexample: A signal that contains uninteresting frequencies up to 6 KHz but whose interesting frequencies are below 4 KHz can be sampled at 10 KHz and later low-passed. The aliasing of components that will be chopped later has no consequence. If such a saving were pointed out to one's colleagues, the reaction, "Oh no! the book says ..." would not be unusual. The more often a partial truth is repeated, the more likely it is to become accepted as the whole truth. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 22, 20052005-02-22
Fred said:>>OK - if we include recursively implemented FIRs then they aren't >>transversal. >>But, that's a special case that only applies to a small subset of FIRs. >>Correct but limited. I like to think of the recursive implementation of >>FIRs as sort of a curiosity with limited application - no matter how cool >>and even valuable some of those implementations may be. Let's not have >>the >>tail wag the dog. >> >>What if we turn it around and say: >>"In some cases a FIR can be implemented recursively and then isn't a >>transversal filter. However, a FIR filter can *always* be implemented as >>a >>sum of delayed inputs and thus, can always be transversal" ?? >>In that sense, FIR can very reasonably imply transversal. >Allan said:> They never should have stopped teaching logic in schools. > > AllanOh geez, now I have to construct a syllogism for testing.... ?? I agree with what you said. Thanks for the clarification - it took me a while. Fred
Reply by ●February 23, 20052005-02-23
"Allan Herriman"> > I assume that 'transversal' is a property of a filter implementation, > whereas 'FIR' is a property of the impulse response of a filter. >I thought that a good summary, and in accord with what much of the literature has used in the past 40 years or so. Neglecting novelty items like recursive FIR implementations, there are other famous nonrecursive structures that also realize Finite Impulse Responses but lack the transversal (tapped-delay) structure. A parallel set of delay lines of different lengths or delays, each weighted at their input or output, and finally summed, is such a structure. (It has been useful in some delay-line technologies that had constraints, for example certain CCD technologies circa the 1970s.) -- Max Hauser
Reply by ●February 23, 20052005-02-23
"Fred Marshall" in news:a9ednW1bu_E7jYTfRVn-iA@centurytel.net...> ... > Before there were truly discrete, digital filters, there were continuous > time or analog filters (such as delay lines) that were "tapped" at > discrete points.Not just _before_ digital filers by the way, but also after. Here are some modern, monolithic continuous-time FIR examples. (Click on "Images" for the figures.) http://tinyurl.com/548jv (Remember: Not all FIR filters are transversal. Not all FIR filters are digital. Not all non-digital FIR filters are even discrete-time.) -------- "To converse at the distance of the Indes by means of sympathetic contrivances may be as natural to future times as to us is a literary correspondance." -- Joseph Glanvill, 1661 [as quoted by Scott Dorsey, news:4723@pyr.gatech.edu, rec.audio, 1988]
Reply by ●February 23, 20052005-02-23
On Wed, 23 Feb 2005 00:52:57 -0800, "Max Hauser" <maxREMOVE@THIStdl.com> wrote:>"Fred Marshall" in news:a9ednW1bu_E7jYTfRVn-iA@centurytel.net... >> ... >> Before there were truly discrete, digital filters, there were continuous >> time or analog filters (such as delay lines) that were "tapped" at >> discrete points. > >Not just _before_ digital filers by the way, but also after. Here are some >modern, monolithic continuous-time FIR examples. (Click on "Images" for the >figures.) > >http://tinyurl.com/548jv > >(Remember: Not all FIR filters are transversal. Not all FIR filters are >digital. Not all non-digital FIR filters are even discrete-time.)A SAW (Surface Acoustic Wave) filter is another good example of a continuous time transversal filter. The surface acoustic waves are launched by "interdigital transducers" which are just interleaved electrodes deposited on the surface of the quartz. The gain (& hence the weight of that 'tap') is proportional to the overlap between the electrodes. http://koigakubo.hitachi.co.jp/~cs/cd/eng/technical/device/saw/ Regards, Allan
Reply by ●February 23, 20052005-02-23
Allan Herriman wrote:> On Wed, 23 Feb 2005 00:52:57 -0800, "Max Hauser" > <maxREMOVE@THIStdl.com> wrote: > > >>"Fred Marshall" in news:a9ednW1bu_E7jYTfRVn-iA@centurytel.net... >> >>>... >>>Before there were truly discrete, digital filters, there were continuous >>>time or analog filters (such as delay lines) that were "tapped" at >>>discrete points. >> >>Not just _before_ digital filers by the way, but also after. Here are some >>modern, monolithic continuous-time FIR examples. (Click on "Images" for the >>figures.) >> >>http://tinyurl.com/548jv >> >>(Remember: Not all FIR filters are transversal. Not all FIR filters are >>digital. Not all non-digital FIR filters are even discrete-time.) > > > > A SAW (Surface Acoustic Wave) filter is another good example of a > continuous time transversal filter. > > The surface acoustic waves are launched by "interdigital transducers" > which are just interleaved electrodes deposited on the surface of the > quartz. The gain (& hence the weight of that 'tap') is proportional > to the overlap between the electrodes. > > http://koigakubo.hitachi.co.jp/~cs/cd/eng/technical/device/saw/ > > Regards, > AllanSAWs are frequency selective depending on the spacing of the electrodes relative to the speed of the wave. If a pulse is launched down the substrate and under a set of electrodes with progressively decreasing spacing, a chirp is produced. When that chirp is applied to to the variable-pitch electrode of an identical device, pulses emerge from its other electrode. Even if the chirps overlap in time, the pulses can be distinct. There are several very useful applications. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 24, 20052005-02-24
Jerry Avins wrote:> Allan Herriman wrote: > >> On Wed, 23 Feb 2005 00:52:57 -0800, "Max Hauser" >> <maxREMOVE@THIStdl.com> wrote: >> >> >>> "Fred Marshall" in news:a9ednW1bu_E7jYTfRVn-iA@centurytel.net... >>> >>>> ... >>>> Before there were truly discrete, digital filters, there were >>>> continuous time or analog filters (such as delay lines) that were >>>> "tapped" at discrete points. >>> >>> >>> Not just _before_ digital filers by the way, but also after. Here >>> are some modern, monolithic continuous-time FIR examples. (Click on >>> "Images" for the figures.) >>> >>> http://tinyurl.com/548jv >>> >>> (Remember: Not all FIR filters are transversal. Not all FIR >>> filters are digital. Not all non-digital FIR filters are even >>> discrete-time.) >> >> >> >> >> A SAW (Surface Acoustic Wave) filter is another good example of a >> continuous time transversal filter. >> >> The surface acoustic waves are launched by "interdigital transducers" >> which are just interleaved electrodes deposited on the surface of the >> quartz. The gain (& hence the weight of that 'tap') is proportional >> to the overlap between the electrodes. >> >> http://koigakubo.hitachi.co.jp/~cs/cd/eng/technical/device/saw/ >> >> Regards, >> Allan > > > SAWs are frequency selective depending on the spacing of the > electrodes relative to the speed of the wave. If a pulse is launched > down the substrate and under a set of electrodes with progressively > decreasing spacing, a chirp is produced. When that chirp is applied to > to the variable-pitch electrode of an identical device, pulses emerge > from its other electrode. Even if the chirps overlap in time, the > pulses can be distinct. There are several very useful applications. > > JerryMany pulse radars used to use that technique for generating and recompressing their chirps. It offers a somewhat limited dynamic range, though, as all SAW devices do. Bulk waves and other side effects of the generation of the surface wave are a key cause. Another is the fact that things don't stop abruptly at the edges of the inter-digital transducers. SAW devices can generally be characterised as reproducable, predictable, stable, but never really great performers. This is getting away from the original issue. The type of SAW device Allan referred to is an exact analogue of a conventional DSP FIR filter, and the same design methods apply to both. The only difference is, the DSP version doesn't require fiddle factors to compensate for the effects around the edges of the transducers. Regards, Steve
Reply by ●February 24, 20052005-02-24
Hello Steve, Max, Allan, Fred, Randy, Jerry, Thank you for all the feedback. The answer could not be clearer! Regards, Hugo
Reply by ●February 24, 20052005-02-24
"Max Hauser" <maxREMOVE@THIStdl.com> wrote in message news:111oecet5h9b407@corp.supernews.com...> "Allan Herriman" >> >.......................A parallel set of delay lines of different lengths >or delays, each weighted at their input or output, and finally summed, is >such a structure. (It has been useful in some delay-line technologies that >had constraints, for example certain CCD technologies circa the 1970s.) > > -- Max HauserMax, A parallel set of delay lines *is* transversal..... Transversal doesn't say anything about "serial" only about "across" which the delay lines of different length accomplish. Fred
