Optimal example filter for essay

Hi, I'm an undergraduate student doing my second course in DSP. I'm
currently writing an essay on "Analysis of digital LTI-filters". 

My plan is to have an example filter and analyze it simply and clearly in
steps in the essay. First I'll start with a flow diagram, then develop a
difference equation, then a impulse response, then a frequency response,
then a transfer function and finally a pole-zero plot. At each of these
steps I will explain the (simple) analysis that can be made with the
equation at hand. 

However, I can't come up with a filter that would be simple enough for me
to actually develop to all these forms, and at the same time would be
complex enough to be analyzed. Does someone have an idea? A difference
equation would be great. 

Most of the sub-forums had names I didn´t even recognize, so I ended up
postin in this part of the forum -- 

i have made a PPT which begins with analysis of unit delay system
and it's properties. from here on i build into a basic 2 tap LPF
and derive all equations for it. including pole zero plot.

let me know if this is of interest to you.

rgds
bharat

On 12/10/2010 09:09 AM, abrotherus wrote:
> Hi, I'm an undergraduate student doing my second course in DSP. I'm
> currently writing an essay on "Analysis of digital LTI-filters".
>
> My plan is to have an example filter and analyze it simply and clearly in
> steps in the essay. First I'll start with a flow diagram, then develop a
> difference equation, then a impulse response, then a frequency response,
> then a transfer function and finally a pole-zero plot. At each of these
> steps I will explain the (simple) analysis that can be made with the
> equation at hand.
>
> However, I can't come up with a filter that would be simple enough for me
> to actually develop to all these forms, and at the same time would be
> complex enough to be analyzed. Does someone have an idea? A difference
> equation would be great.
>
> Most of the sub-forums had names I didn´t even recognize, so I ended up
> postin in this part of the forum --

(aside): I hope that this is for a technical writing class, and not one 
of your main-line engineering courses!  Teaching you to communicate is 
all well and good, but you still need to be able to do the _work_ that 
you're communicating _about_!

Normally when one is working with filters one proceeds in the opposite 
direction: one conceives of performance criteria, then one finds a 
frequency- or time-domain description that meets those criteria, then 
one designs a filter that meets (or at least approximates) them, etc.

Of course, one is confronted often enough with a working (or almost 
working) product that has some poorly-commented code (perhaps the 
ever-informative "// implement a filter" and nothing else) that one must 
then unwind back to performance specifications.

Why don't you just design a 4- or 6-pole lowpass IIR filter, realize it 
in cascaded 2nd-order direct-form sections, then do your analysis?  If 
you're writing an essay about it then (I hope!!!) the main thrust of the 
lesson is to make sure you can coherently communicate what the heck 
you're doing -- unless the prof gave you some design criteria then he 
doesn't want to test your design chops in this one.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

On Dec 10, 10:09=A0am, "abrotherus"
<anders.brotherus@n_o_s_p_a_m.mac.com> wrote:
> Hi, I'm an undergraduate student doing my second course in DSP. I'm
> currently writing an essay on "Analysis of digital LTI-filters".
>
> My plan is to have an example filter and analyze it simply and clearly in
> steps in the essay. First I'll start with a flow diagram, then develop a
> difference equation, then a impulse response, then a frequency response,
> then a transfer function and finally a pole-zero plot. At each of these
> steps I will explain the (simple) analysis that can be made with the
> equation at hand.
>
> However, I can't come up with a filter that would be simple enough for me
> to actually develop to all these forms, and at the same time would be
> complex enough to be analyzed. Does someone have an idea? A difference
> equation would be great.
>
> Most of the sub-forums had names I didn=B4t even recognize, so I ended up
> postin in this part of the forum --

It sounds like you're trying to convey simple DSP concepts to the
layman. If so, using a simple moving average (simple difference
equation with unity taps). Most people (outside of DSP) have used it
directly, or without knowing, but everyone is familiar with the
concept of averaging. It can be complex (to you audience) if you go
into enough detail in both domains.

Bryan

On 12/10/2010 09:46 AM, Bryan wrote:
> On Dec 10, 10:09 am, "abrotherus"
> <anders.brotherus@n_o_s_p_a_m.mac.com>  wrote:
>> Hi, I'm an undergraduate student doing my second course in DSP. I'm
>> currently writing an essay on "Analysis of digital LTI-filters".
>>
>> My plan is to have an example filter and analyze it simply and clearly in
>> steps in the essay. First I'll start with a flow diagram, then develop a
>> difference equation, then a impulse response, then a frequency response,
>> then a transfer function and finally a pole-zero plot. At each of these
>> steps I will explain the (simple) analysis that can be made with the
>> equation at hand.
>>
>> However, I can't come up with a filter that would be simple enough for me
>> to actually develop to all these forms, and at the same time would be
>> complex enough to be analyzed. Does someone have an idea? A difference
>> equation would be great.
>>
>> Most of the sub-forums had names I didn&#4294967295;t even recognize, so I ended up
>> postin in this part of the forum --
>
> It sounds like you're trying to convey simple DSP concepts to the
> layman. If so, using a simple moving average (simple difference
> equation with unity taps). Most people (outside of DSP) have used it
> directly, or without knowing, but everyone is familiar with the
> concept of averaging. It can be complex (to you audience) if you go
> into enough detail in both domains.

I remember once trying to explain to a person with a computer science 
background why a moving average filter was a Really Bad Thing to have 
inside a control loop.  Eventually I managed to find terminology that 
made sense*, but it wasn't easy.

We used a first-order IIR low-pass -- things worked just fine.

* I told her that moving average filters give you a lot more delay than 
they give you attenuation.  I could have said "it's not minimum phase", 
except that (a) I hadn't really related that term to that filter at that 
time, and (b) it would have been even more mumbo-jumbo for her.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

On 12/10/2010 9:09 AM, abrotherus wrote:
> Hi, I'm an undergraduate student doing my second course in DSP. I'm
> currently writing an essay on "Analysis of digital LTI-filters".
>
> My plan is to have an example filter and analyze it simply and clearly in
> steps in the essay. First I'll start with a flow diagram, then develop a
> difference equation, then a impulse response, then a frequency response,
> then a transfer function and finally a pole-zero plot. At each of these
> steps I will explain the (simple) analysis that can be made with the
> equation at hand.
>
> However, I can't come up with a filter that would be simple enough for me
> to actually develop to all these forms, and at the same time would be
> complex enough to be analyzed. Does someone have an idea? A difference
> equation would be great.
>
> Most of the sub-forums had names I didn´t even recognize, so I ended up
> postin in this part of the forum --
>
>

If you want to communicate nicely the once you've said "difference 
equation" (rather than "differential equation") then you should be 
saying "unit sample response" and not "impulse response".

I think that IIR filter equations will be more interesting although my 
first thought was a simple FIR:
[0.5   1.0   0.5]

Nonetheless, I'd keep the filter very simple / small order.

Fred

Tim Wescott wrote:


> I remember once trying to explain to a person with a computer science 
> background why a moving average filter was a Really Bad Thing to have 
> inside a control loop.

I hear you. I had difficult time explaining that making control loop 
faster would provide for more accurate control. "How is it? You are 
obviously throwing more jitter in a loop..."

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

abrotherus wrote:

> Hi, I'm an undergraduate student doing my second course in DSP. I'm
> currently writing an essay on "Analysis of digital LTI-filters". 
> 
> My plan is to have an example filter and analyze it simply and clearly in
> steps in the essay. First I'll start with a flow diagram, then develop a
> difference equation, then a impulse response, then a frequency response,
> then a transfer function and finally a pole-zero plot. At each of these
> steps I will explain the (simple) analysis that can be made with the
> equation at hand. 
> However, I can't come up with a filter that would be simple enough for me
> to actually develop to all these forms, and at the same time would be
> complex enough to be analyzed. Does someone have an idea? A difference
> equation would be great. 

Consider a basic pole only filter of the second order with a given Q.
Normalize filter to the unity DC gain and unity noise bandwidth.
Apply a unity step function to the input.
Determine the time at which the filter output settles within +/- X 
percent of the final value of 1 (depending on Q).
Now, define what would be the value of Q for the fastest settling to a 
given X.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

abrotherus <anders.brotherus@n_o_s_p_a_m.mac.com> wrote:
> Hi, I'm an undergraduate student doing my second course in DSP. I'm
> currently writing an essay on "Analysis of digital LTI-filters". 

(snip)

Note for others.  It is best to state up front that it is a school
project, such that you get appropriate replies.

There is nothing wrong with asking for help with school work,
except when you don't say that it is school work.  

(Especially note that for students with Canadian helicopters.)

-- glen

On 12/10/2010 01:53 PM, glen herrmannsfeldt wrote:
> abrotherus<anders.brotherus@n_o_s_p_a_m.mac.com>  wrote:
>> Hi, I'm an undergraduate student doing my second course in DSP. I'm
>> currently writing an essay on "Analysis of digital LTI-filters".
>
> (snip)
>
> Note for others.  It is best to state up front that it is a school
> project, such that you get appropriate replies.
>
> There is nothing wrong with asking for help with school work,
> except when you don't say that it is school work.
>
> (Especially note that for students with Canadian helicopters.)

Note, too, that he starts with a plan and not a blank sheet, and that 
he's not just copying down his homework question verbatim -- both of 
these are signs that he's actively thinking.

Of course, if someone came on and said "I'm in my second course in DSP, 
and on this week's homework the prof asked <...>.  I'm totally lost! 
What does this mean!  Help!"  I think that we'd at least chip in and 
explain the _question_ to him (and point out that teaching assistants 
get paid* for a reason).

* Not that they get paid _much_.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html