filter impuse response

Sirs,

I would like to know if obsevration of impulse response of a filter gives
some clue the type of filter it is (low pass, high pass).

For example, I am seeing impulse response of a filer which is a LPF. The
impulse response is just a damping sinusoidal waveform.

Thanks,

On 12/9/12 10:17 AM, manishp wrote:
>
> I would like to know if observation of impulse response of a filter gives
> some clue the type of filter it is (low pass, high pass).
>
> For example, I am seeing impulse response of a filer which is a LPF. The
> impulse response is just a damping sinusoidal waveform.
>

this is actually a pretty good question.

seeing a sinusoid ringing in the filter impulse response should clue you 
in to some amount of resonance, but it's hard to tell if it's a LPF or 
BPF just from that.

let's assume that polarity is not an issue.  if you can tell there's a 
lot more "positive area" in the impulse response than "negative area", 
it's gonna be a LPF.  if the positive and negative area is about the 
same, but the sign of the samples do not alternate each adjacent sample, 
then it's a BPF.  if the signs of the samples alternate every sample, 
then it's a HPF.

but there are BPF or HPF impulse responses that would be hard to spot, 
just by looking at them.  kinda hard doing a Fourier Transform in one's 
head.

i dunno how i would spot a notch filter.  i guess i'll have to check 
with MATLAB (or Octave, but i can't get my Octave graphics to work). 
that's something i might recommend for you to do.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

>On 12/9/12 10:17 AM, manishp wrote:
>>
>> I would like to know if observation of impulse response of a filter
gives
>> some clue the type of filter it is (low pass, high pass).
>>
>> For example, I am seeing impulse response of a filer which is a LPF.
The
>> impulse response is just a damping sinusoidal waveform.
>>
>
>this is actually a pretty good question.
>
>seeing a sinusoid ringing in the filter impulse response should clue you 
>in to some amount of resonance, but it's hard to tell if it's a LPF or 
>BPF just from that.
>
>let's assume that polarity is not an issue.  if you can tell there's a 
>lot more "positive area" in the impulse response than "negative area", 
>it's gonna be a LPF.  if the positive and negative area is about the 
>same, but the sign of the samples do not alternate each adjacent sample, 
>then it's a BPF.  if the signs of the samples alternate every sample, 
>then it's a HPF.
>
>but there are BPF or HPF impulse responses that would be hard to spot, 
>just by looking at them.  kinda hard doing a Fourier Transform in one's 
>head.
>
>i dunno how i would spot a notch filter.  i guess i'll have to check 
>with MATLAB (or Octave, but i can't get my Octave graphics to work). 
>that's something i might recommend for you to do.
>
>
>-- 
>
>r b-j                  rbj@audioimagination.com
>
>"Imagination is more important than knowledge."
>

I used to tell even the cutoff point but it was always wrong.

Kadhiem

On Sun, 09 Dec 2012 22:43:36 -0500, robert bristow-johnson
<rbj@audioimagination.com> wrote:

>let's assume that polarity is not an issue.  if you can tell there's a 
>lot more "positive area" in the impulse response than "negative area", 
>it's gonna be a LPF.  

To formalize; if the area under the curve (integral of the impulse
response of a continuous time filter; sum of the samples of a
discrete time filter) is nonzero, then the filter has a general
lowpass characteristic.

>if the positive and negative area is about the 
>same, but the sign of the samples do not alternate each adjacent sample, 
>then it's a BPF.  if the signs of the samples alternate every sample, 
>then it's a HPF.

Hmm ... I think I have a counterexample: build a frequency domain
digital filter in which the filter gain in every bin is magnitude
"1" phase "0" -- except for the bin corresponding to half the
sampling frequency, at which the filter gain is "0". The result
will be a lowpass filter in which the impulse response alternates
sign every sample.

Continuous time highpass filters are difficult to discern from the
impulse response, but with discrete time filters if you change the
sign of every other sample of the impulse response (equivalent to
multiplying by exp[jnPI] -- think about the resulting frequency
domain shift that results) and then sum the result over all
samples of the impulse response, and that sum is nonzero, then it
is a highpass filter.

Again, for digital filters only, if both of the above yield sums
of zero, then it is a bandpass filter. I don't think that an
equivalent test exists for analog filters.

>i dunno how i would spot a notch filter.  i guess i'll have to check 
>with MATLAB (or Octave, but i can't get my Octave graphics to work). 
>that's something i might recommend for you to do.

A notch filter is just [1 - (a bandpass filter)], so if both tests
above (digital filter only) are nonzero, then the filter has a
general bandstop characteristic.

Greg

On Monday, December 10, 2012 10:07:40 AM UTC-6, Greg Berchin wrote:

> Continuous time highpass filters are difficult to discern from the
> impulse response

What was I thinking? If the integral of the impulse response is zero, then the filter has a general highpass (or possibly bandpass) response.

Greg

On 12/10/12 11:52 AM, Greg Berchin wrote:
> On Monday, December 10, 2012 10:07:40 AM UTC-6, Greg Berchin wrote:
>
>> Continuous time highpass filters are difficult to discern from the
>> impulse response
>
> What was I thinking? If the integral of the impulse response is zero, then the filter has a general highpass (or possibly bandpass) response.

what i was thinking (and my whole answer is essentially a guess from my 
own experience) is that an HPF will be an LPF modulated up to Nyquist. 
that's why i would expect most (not all) samples to have the opposite 
sign that their adjacent neighbors have.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Monday, December 10, 2012 10:52:06 AM UTC-6, Greg Berchin wrote:

> 
> What was I thinking? If the integral of the impulse response is zero, then the filter has a general highpass (or possibly bandpass) response.
> 


The integral of the impulse response h(t),
that is, the total area under h(t), is 
**exactly** equal to the value of the 
transfer function H(f) at f = 0, in other
words, the response to DC. So, if H(0) = 0
**exactly**, then we have an (idealized)
bandpass or highpass filter.  More practically, 
H(f) will be **very small**, but not identically 
0 (or within round-off error if numerical
integration is being done), for a BPF or HPF.
All BPFs and HPFs have (negligibly) small
DC responses, just as all real LPFs have
(negligibly) small responses at high 
frequencies.

Dilip Sarwate

dvsarwate <dvsarwate@yahoo.com> wrote:
> On Monday, December 10, 2012 10:52:06 AM UTC-6, Greg Berchin wrote:
 
>> What was I thinking? If the integral of the impulse response is 
>> zero, then the filter has a general highpass (or possibly bandpass) 
>> response.
 
> The integral of the impulse response h(t),
> that is, the total area under h(t), is 
> **exactly** equal to the value of the 
> transfer function H(f) at f = 0, in other
> words, the response to DC. So, if H(0) = 0
> **exactly**, then we have an (idealized)
> bandpass or highpass filter.  More practically, 
> H(f) will be **very small**, but not identically 
> 0 (or within round-off error if numerical
> integration is being done), for a BPF or HPF.

For an FIR filter, it shouldn't be hard to make an
ideal DC (f=0) blocking filter. 

For an analog filter, it seems to me to depend on
how good a capacitor you can make. Seems to me that
isn't so much of a problem.

> All BPFs and HPFs have (negligibly) small
> DC responses, just as all real LPFs have
> (negligibly) small responses at high 
> frequencies.

It gets more interesting at high frequencies. 

There aren't any real practical tests for f=infinity,
but usually a frequency higher than any that the system
needs to respond to is high enough. For audio, that might
be 30kHz, or (for us who aren't babies) maybe 20kHz is enough.

For video, maybe 200MHz or so should be enough.

Also, it seems to me that the first place where h(t) crosses
zero should be related to its filter cutoff frequency.

Otherwise, just compute H(f) from h(t).

-- glen

On 12/10/12 5:57 PM, dvsarwate wrote:
>
> All BPFs and HPFs have (negligibly) small
> DC responses, just as all real LPFs have
> (negligibly) small responses at high
> frequencies.

i don't think that's true, Dilip.  want some counter-examples?  (i'll 
bet you can figure out some counter-examples.)

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Sun, 09 Dec 2012 22:43:36 -0500, robert bristow-johnson wrote:

> On 12/9/12 10:17 AM, manishp wrote:
>>
>> I would like to know if observation of impulse response of a filter
>> gives some clue the type of filter it is (low pass, high pass).
>>
>> For example, I am seeing impulse response of a filer which is a LPF.
>> The impulse response is just a damping sinusoidal waveform.
>>
>>
 <snip>
> but there are BPF or HPF impulse responses that would be hard to spot,
> just by looking at them.  kinda hard doing a Fourier Transform in one's
> head.

In particular, if you're sampling much faster than the frequency of 
interest you may have a combination of a high pass filter followed by 
"high frequency rolloff".  You'd get an overall characteristic that's 
bandpass, but with disjoint poles and with notation in the system design 
to the effect "here be high pass" and "here be rolloff".

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com