# Definition for transversal equalizers

Started by February 20, 2005
```Hello Everyone,

Can anyone point me the definition for a transversal equalizer? Some
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

```
```"huke" <hugo.harada@gmail.com> wrote in message
> 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
>

Before there were truly discrete, digital filters, there were continuous
time or analog filters (such as delay lines) that were "tapped" at
discrete
points.  The signal input appeared in delayed versions: it transversed in
time (i.e. "went across") as you viewed or accessed the delay line taps at

one instant of time.

From an anlysis point of view, a transversal filter and a FIR filter can be
viewed as the same thing.
The frequency response is periodic in the inverse of the (assumed regular)
tap separation in time.

A transversal equalizer is a transversal filter (or FIR filter) that usually
has adjustable weights / coefficients in the filter so that the equalization
can be adjusted for best performance.  In the latest IEEE Spectrum there is
an article by or about Bernie Widrow who pioneered LMS adaptive filters.
The article mentions Robert Lucky's work at Bell Labs that preceded on
adaptive equalizers.  There are many ways and many objective criterion for

So, just substitute "FIR" for "transversal" and you should be
OK.  And, yes,
usually linear - although modifying the coefficients very rapidly could
cause the filter to become "nonlinear" during the change.

Fred

```
```Hi Fred,

Thank you very much for your valuable input.

I really appreciated it.

Hugo

```
```"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."
--
%  Randy Yates                  % "The dreamer, the unwoken fool -
%% Fuquay-Varina, NC            %  in dreams, no pain will kiss the brow..."
%%% 919-577-9882                %
```
```On Mon, 21 Feb 2005 14:08:08 GMT, Randy Yates <yates@ieee.org> wrote:

>
>> 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.

Regards,
Allan
```
```"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:
>
>>
>>> 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.

Fred

```
```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:
>>
>>>
>>>> Hello Everyone,
>>>>
>>>> Can anyone point me the definition for a transversal equalizer?
Some
>>>> books only treat linear and adaptive equalizers, and some talk
>>>> 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

Regards,
Allan
```
```Allan Herriman <allan.herriman.hates.spam@ctam.com.au.invalid> writes:
> [...]
> 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

This is not equivalent to the recursive implementation given above. I
think you meant to write something like

n
y[n] = sum  x[m].
m = n-k+1

However, I agree with your point.
--
%  Randy Yates                  % "Remember the good old 1980's, when
%% Fuquay-Varina, NC            %  things were so uncomplicated?"
%%% 919-577-9882                % 'Ticket To The Moon'
%%%% <yates@ieee.org>           % *Time*, Electric Light Orchestra
```
```On Tue, 22 Feb 2005 03:34:13 GMT, Randy Yates <yates@ieee.org> wrote:

>Allan Herriman <allan.herriman.hates.spam@ctam.com.au.invalid> writes:
>> [...]
>> 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
>
>This is not equivalent to the recursive implementation given above. I
>think you meant to write something like
>
>         n
> y[n] = sum  x[m].
>       m = n-k+1

Yes indeed!  My brain starts to fade around six in the morning, at
which time the little pixies help me with my news postings.

Regards,
Allan
```
```"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:
>>>
>>>>
>>>>> Hello Everyone,
>>>>>
>>>>> Can anyone point me the definition for a transversal equalizer?
Some
>>>>> books only treat linear and adaptive equalizers, and some talk
>>>>> 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.

Fred

```
```"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:0fednQVKW-v_DoPfRVn-og@centurytel.net...
>
> "Max Hauser" <maxREMOVE@THIStdl.com> wrote in message
> news:111oecet5h9b407@corp.supernews.com...
>> "Allan Herriman"
>>>
>>
>> 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
>
> In the olden days when delay lines of any appreciable length were
> expensive we used a relatively wideband torsional wire acoustic delay line
> over the range 100kHz to 1MHz.  The line wasn't tapped.  We wanted to
> delay signals up to 100kHz or so and create a FIR filter sort of response.
> So, we used frequency domain multiplexing on the line and used the line
> multiple times:
>
> output at baseband at t
> first pass at 150kHz downtranslate a tap out at t+T
> uptranslate for:
> second pass at 300kHz, downtranslate a tap out at t+2T
> upstranslate for:
> third pass at 450kHz, downtranslate a tap out at t+3T
>
> End result, one delay element of length T for a FIR filter of length 4.
> So, in a way, these were different length delay lines in parallel even
> though the physical line was the same one.
> Note that this isn't recursive because all the signal paths are
> independent / not added - well they are added in the delay line but
> separated in frequency so the end result is not recursive.
>
> Fred

Well, on second thought, it seems that this implementation was more serial
than parallel.

Fred

```
```"Max Hauser" <maxREMOVE@THIStdl.com> wrote in message
news:111oecet5h9b407@corp.supernews.com...
> "Allan Herriman"
>>
>
> 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

In the olden days when delay lines of any appreciable length were expensive
we used a relatively wideband torsional wire acoustic delay line over the
range 100kHz to 1MHz.  The line wasn't tapped.  We wanted to delay signals
up to 100kHz or so and create a FIR filter sort of response.  So, we used
frequency domain multiplexing on the line and used the line multiple times:

output at baseband at t
first pass at 150kHz downtranslate a tap out at t+T
uptranslate for:
second pass at 300kHz, downtranslate a tap out at t+2T
upstranslate for:
third pass at 450kHz, downtranslate a tap out at t+3T

End result, one delay element of length T for a FIR filter of length 4.
So, in a way, these were different length delay lines in parallel even
though the physical line was the same one.
Note that this isn't recursive because all the signal paths are independent
/ not added - well they are added in the delay line but separated in
frequency so the end result is not recursive.

Fred

```
```"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 Hauser

Max,

A parallel set of delay lines *is* transversal.....
"across" which
the delay lines of different length accomplish.

Fred

```
```Hello Steve, Max, Allan, Fred, Randy, Jerry,

Thank you for all the feedback. The answer could not be clearer!

Regards,

Hugo

```
```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.
>
> Jerry

Many 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
```
```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.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```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
```
```"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]

```
```"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

```
```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.
>
> Allan

Oh 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

```