Nonlinear phase FIR filter in Matlab based on step response

Hi,

I'm a biologist so I don't have much experience designing filters, but
I think I need to apply a filter to some time series data in order to
model a biological system.

The problem:
I know the step response of the system and I need to design a filter
based on this.  The best way I can describe the step response is that
it has a logarithmic-like rise that saturates.  Based on my cursory
understanding of signal processing, this makes me think that I need a
non-linear phase filter (since the step response is not symmetric).
Also, because I'm trying to model a biological system it's important
to use a casual filter.  To add some more complexity, the system has
different step responses, depending on the polarity of the step.  The
general shape of the curve is the same, but the time constants are
different.  So for instance, the time constant is 230 msec for
positive steps, 80 msec for negative.

Once the filter is designed, I will test its response to different
(non-step) inputs in order to evaluate the performance of the model.

My questions:
1. Is it even possible to design such a filter?
2. If so, how would I go about implementing it in Matlab using the
filter() function (I don't have the filter toolbox)?
3. Do you have any recommendations for places I can find more
information on this topic, preferably without too many equations (I
know, I know....)?  I've been using the Second Edition of Steven
Smith's "The Scientist and Engineer's Guide to DSP," but it doesn't
really cover the specifics of what I'm after.

Assume a 1 KHz sampling rate.  If needed, I can post some of the
data.


The details (if you're interested):
I'm recording action potentials (spikes) from nerve cells (neurons) in
the brain and attempting to model their response to an input.  There
are many ways to define the response of a neuron, but what I'm looking
at specifically is called the instantaneous firing rate, which is the
reciprocal of the time between consecutive spikes.  The neurons I'm
recording have a baseline firing rate around 20 spikes/sec and can
increase or decrease their firing rate from that baseline, depending
on their input.  The dynamics of their response are governed by both
their intrinsic properties and their inputs.  All neurons can be
considered filters to some extent, but there's reason to believe that
the ones I'm studying have some unique filtering characteristics.

TIA,
shane

sheiney@gmail.com wrote:
> 
> Hi,
> 
> I'm a biologist so I don't have much experience designing filters, but
> I think I need to apply a filter to some time series data in order to
> model a biological system.
> 
> The problem:
> I know the step response of the system and I need to design a filter
> based on this.  The best way I can describe the step response is that
> it has a logarithmic-like rise that saturates.

The best way to describe the step response would have been to reveal
whether you are talking about digital or analog. It also would be
helpful to know if by "step" you mean the data starts at a constant
level and ends at a constant level. That is, is this so called "step"
finite or does it go on forever.

You did mention time series data (I'm not sure if that is a reference to
the step response or something else) so I will assume everything is
digital and finite. So extracting the impulse rsponse from your Step
response is simply a matter of finding the difference between each
sample in the data. Assuming the data in question isn't humongous you
could do that with paper and pencil.
	The impulse response will be your FIR filter coefficients.

	You also said something about "saturates". That sounds like it could be
a problem because the best you can do is just guess what is going on
there.


-jim


>  Based on my cursory
> understanding of signal processing, this makes me think that I need a
> non-linear phase filter (since the step response is not symmetric).

> Also, because I'm trying to model a biological system it's important
> to use a casual filter.  To add some more complexity, the system has
> different step responses, depending on the polarity of the step.  The
> general shape of the curve is the same, but the time constants are
> different.  So for instance, the time constant is 230 msec for
> positive steps, 80 msec for negative.
> 
> Once the filter is designed, I will test its response to different
> (non-step) inputs in order to evaluate the performance of the model.
> 
> My questions:
> 1. Is it even possible to design such a filter?
> 2. If so, how would I go about implementing it in Matlab using the
> filter() function (I don't have the filter toolbox)?
> 3. Do you have any recommendations for places I can find more
> information on this topic, preferably without too many equations (I
> know, I know....)?  I've been using the Second Edition of Steven
> Smith's "The Scientist and Engineer's Guide to DSP," but it doesn't
> really cover the specifics of what I'm after.
> 
> Assume a 1 KHz sampling rate.  If needed, I can post some of the
> data.
> 
> The details (if you're interested):
> I'm recording action potentials (spikes) from nerve cells (neurons) in
> the brain and attempting to model their response to an input.  There
> are many ways to define the response of a neuron, but what I'm looking
> at specifically is called the instantaneous firing rate, which is the
> reciprocal of the time between consecutive spikes.  The neurons I'm
> recording have a baseline firing rate around 20 spikes/sec and can
> increase or decrease their firing rate from that baseline, depending
> on their input.  The dynamics of their response are governed by both
> their intrinsic properties and their inputs.  All neurons can be
> considered filters to some extent, but there's reason to believe that
> the ones I'm studying have some unique filtering characteristics.
> 
> TIA,
> shane

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> The best way to describe the step response would have been to reveal
> whether you are talking about digital or analog. It also would be
> helpful to know if by "step" you mean the data starts at a constant
> level and ends at a constant level. That is, is this so called "step"
> finite or does it go on forever.

I'm talking about an originally analog signal that has been digitally
sampled, so it is now a digital (finite) signal.  Sorry for not making
that more clear from the beginning.  By "step" I mean that the system
starts at a constant level, receives a step input with a finite
amplitude, and ends at a new constant level.  The output of the system
to this step input is what I'm considering the "step response."  I
tried to use the correct terminology for signal processing, but I'm
new to this so I could have gotten it wrong.  If what you're asking is
whether the step is a "pulse" with finite length or simply a level
change, I guess I would consider it more of a level change.  That is,
for the time course that I'm interested in, the step length can be
considered infinite.

> You did mention time series data (I'm not sure if that is a reference to
> the step response or something else) so I will assume everything is
> digital and finite. So extracting the impulse rsponse from your Step
> response is simply a matter of finding the difference between each
> sample in the data. Assuming the data in question isn't humongous you
> could do that with paper and pencil.
>         The impulse response will be your FIR filter coefficients.

Thanks for the suggestion.  I just tried this and it couldn't quite
predict how the system responds to arbitrary input (which is my goal),
so I guess I need to take into account some other factor or factors.
What I did was to take the "diff" of my "step response" and use that
as b in the filter() function:

>>y=filter(b,1,x)

where x is my arbitrary input and y is the predicted output of the
system.  Then I plotted y alongside the actual output to evaluate the
quality of the prediction.  The actual output changed slower than the
predicted output and was less sensitive to transients in the input.

I'm not sure exactly what the system is doing (that's why I'm trying
to model it), but my impression is that it might be serving as
something akin to a bandpass filter for a relatively narrow range of
frequencies.  But it might also be doing something else, because it
responds faster to negative steps of the input than to positive
steps.  Can anyone think of something analogous in the engineering
world, possibly from control systems?  I just don't have the expertise
to recognize it.

>         You also said something about "saturates". That sounds like it could be
> a problem because the best you can do is just guess what is going on
> there.

What I mean by "saturates" is not that the analog to digital
conversion has saturated.  The data at the saturation point are real.
It just seems to mean that once the system (a neuron) has reached a
certain point, it is unable to increase its response to further
input.  This is quite common in neurophysiology because of the
inherent properties of neurons (something called the refractory period
of action potentials).  I'm just not sure how to model this with a
filter.  Do you know of a good resource that I could look to for
hints?

Thanks,
shane

sheiney wrote:
> 
> > The best way to describe the step response would have been to reveal
> > whether you are talking about digital or analog. It also would be
> > helpful to know if by "step" you mean the data starts at a constant
> > level and ends at a constant level. That is, is this so called "step"
> > finite or does it go on forever.
> 
> I'm talking about an originally analog signal that has been digitally
> sampled, so it is now a digital (finite) signal.  Sorry for not making
> that more clear from the beginning.  By "step" I mean that the system
> starts at a constant level, receives a step input with a finite
> amplitude, and ends at a new constant level.  The output of the system
> to this step input is what I'm considering the "step response."  I
> tried to use the correct terminology for signal processing, but I'm
> new to this so I could have gotten it wrong.  If what you're asking is
> whether the step is a "pulse" with finite length or simply a level
> change, I guess I would consider it more of a level change.  That is,
> for the time course that I'm interested in, the step length can be
> considered infinite.

I was trying to determine if your impulse response was infinite or
finite. It needs to be finite to get an FIR filter. If it starts at one
level and ends at some level then what is in between is the step. When
you subtract each sample from its neighbor to get the impulse response
the part of the data that is constant will produce a difference that is
zero. 


> 
> > You did mention time series data (I'm not sure if that is a reference to
> > the step response or something else) so I will assume everything is
> > digital and finite. So extracting the impulse rsponse from your Step
> > response is simply a matter of finding the difference between each
> > sample in the data. Assuming the data in question isn't humongous you
> > could do that with paper and pencil.
> >         The impulse response will be your FIR filter coefficients.
> 
> Thanks for the suggestion.  I just tried this and it couldn't quite
> predict how the system responds to arbitrary input (which is my goal),
> so I guess I need to take into account some other factor or factors.
> What I did was to take the "diff" of my "step response" and use that
> as b in the filter() function:
> 
> >>y=filter(b,1,x)

So you feed your system a step input and you record the output? Is that
what you did to get the data from which you derived b ? 

> 
> where x is my arbitrary input and y is the predicted output of the
> system.  Then I plotted y alongside the actual output to evaluate the
> quality of the prediction.  The actual output changed slower than the
> predicted output and was less sensitive to transients in the input.
> 
> I'm not sure exactly what the system is doing (that's why I'm trying
> to model it), but my impression is that it might be serving as
> something akin to a bandpass filter for a relatively narrow range of
> frequencies.  But it might also be doing something else, because it
> responds faster to negative steps of the input than to positive
> steps.  Can anyone think of something analogous in the engineering
> world, possibly from control systems?  I just don't have the expertise
> to recognize it.

It sounds like the system is not strictly linear. 


> 
> >         You also said something about "saturates". That sounds like it could be
> > a problem because the best you can do is just guess what is going on
> > there.
> 
> What I mean by "saturates" is not that the analog to digital
> conversion has saturated.  The data at the saturation point are real.
> It just seems to mean that once the system (a neuron) has reached a
> certain point, it is unable to increase its response to further
> input. 

This also doesn't sound like it is not linear.

	 If it is not linear than it could be complicated to model or it could
be fairly simple. If it were linear you should be able to determine what
it is from just what you already have. But since it probably isn't
linear you probably need to do a lot more work. I would first try seeing
how it responds to different amounts of step. Big step, little step,
medium sized step - like that. If it is linear it shouldn't make any
difference other than the scale of the output ( i. e. the scale of b
would change proportional to the scale of the input steps).

-jim

> This is quite common in neurophysiology because of the
> inherent properties of neurons (something called the refractory period
> of action potentials).  I'm just not sure how to model this with a
> filter.  Do you know of a good resource that I could look to for
> hints?
> 
> Thanks,
> shane

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On Jul 20, 7:11 pm, shei...@gmail.com wrote:
> Hi,
>
> I'm a biologist so I don't have much experience designing filters, but
> I think I need to apply a filter to some time series data in order to
> model a biological system.
>
> The problem:
> I know the step response of the system and I need to design a filter
> based on this.  The best way I can describe the step response is that
> it has a logarithmic-like rise that saturates.  Based on my cursory
> understanding of signal processing, this makes me think that I need a
> non-linear phase filter (since the step response is not symmetric).
> Also, because I'm trying to model a biological system it's important
> to use a casual filter.  To add some more complexity, the system has
> different step responses, depending on the polarity of the step.  The
> general shape of the curve is the same, but the time constants are
> different.  So for instance, the time constant is 230 msec for
> positive steps, 80 msec for negative.
[snip]

Shane,

To back off a bit, when you are trying to model a system as a filter,
in the sense that the input-output is described by a convolution,
you are already implicitly assuming that the system is linear and
time-invariant.  Do you think that this is the case?  Just wondering
out loud, since you didn't explain this part in your original post.

Julius

On Jul 22, 11:25 am, julius <juli...@gmail.com> wrote:
> On Jul 20, 7:11 pm, shei...@gmail.com wrote:
>
> > Hi,
>
> > I'm a biologist so I don't have much experience designing filters, but
> > I think I need to apply a filter to some time series data in order to
> > model a biological system.
>
> > The problem:
> > I know the step response of the system and I need to design a filter
> > based on this.  The best way I can describe the step response is that
> > it has a logarithmic-like rise that saturates.  Based on my cursory
> > understanding of signal processing, this makes me think that I need a
> > non-linear phase filter (since the step response is not symmetric).
> > Also, because I'm trying to model a biological system it's important
> > to use a casual filter.  To add some more complexity, the system has
> > different step responses, depending on the polarity of the step.  The
> > general shape of the curve is the same, but the time constants are
> > different.  So for instance, the time constant is 230 msec for
> > positive steps, 80 msec for negative.
>
> [snip]
>
> Shane,
>
> To back off a bit, when you are trying to model a system as a filter,
> in the sense that the input-output is described by a convolution,
> you are already implicitly assuming that the system is linear and
> time-invariant.  Do you think that this is the case?  Just wondering
> out loud, since you didn't explain this part in your original post.
>
> Julius

If I could I would feed white noise into the system rather than a step
and take the power spectral density of the output -and average of
course over time. Assuming minimum phase you could get the transfer
function of the system. All assuming it is approx linear I suppose
which giving it is biological it most probably is not.

Thanks for your responses.

I had hoped that the system would be "linear enough," but this seems
to be turning out to not be the case.  In a way, that makes it more
interesting :-)  The story is actually a little more complicated than
I initially let on in that I don't actually have total control over
the input to the system.  The "input" that I have been referring to is
actually a behavioral output that may be getting fed into the neuron
through a collateral brain pathway.  It's somewhat complex, which is
why I didn't explain the problem in this way initially, but what I'm
actually looking for is a correlation between the behavioral output
and the response of the neuron.  There seems to be a high correlation
between the behavior and the neuron in some respects, but the dynamics
of the behavior and the neuron response are different, which is why I
thought trying to model the neuron as a filter of the
"input" (behavior) might be fruitful.

Despite not having total control of the input to the neuron, I can
control the behavior in some ways.  I can make it a "step" of
different amplitudes or I can make it sinusoidal (within a limited
frequency range).  I can also probably do some arbitrary waveforms.
However, white noise wouldn't be possible because of the limited
bandwidth of the behavior.  Accordingly, the "step" isn't really a
true step in that it takes about 50 msec to get to the new level.  But
this point is probably moot if the neuron isn't linear, which is how
things are looking.

Jim, you mentioned that even if the system isn't linear it could
possibly still be simple to model.  How might I go about determining
whether this is the case?

shane

On Jul 22, 12:09 am, gyansor...@gmail.com wrote:
> On Jul 22, 11:25 am, julius <juli...@gmail.com> wrote:
>
>
>
> > On Jul 20, 7:11 pm, shei...@gmail.com wrote:
>
> > > Hi,
>
> > > I'm a biologist so I don't have much experience designing filters, but
> > > I think I need to apply a filter to some time series data in order to
> > > model a biological system.
>
> > > The problem:
> > > I know the step response of the system and I need to design a filter
> > > based on this.  The best way I can describe the step response is that
> > > it has a logarithmic-like rise that saturates.  Based on my cursory
> > > understanding of signal processing, this makes me think that I need a
> > > non-linear phase filter (since the step response is not symmetric).
> > > Also, because I'm trying to model a biological system it's important
> > > to use a casual filter.  To add some more complexity, the system has
> > > different step responses, depending on the polarity of the step.  The
> > > general shape of the curve is the same, but the time constants are
> > > different.  So for instance, the time constant is 230 msec for
> > > positive steps, 80 msec for negative.
>
> > [snip]
>
> > Shane,
>
> > To back off a bit, when you are trying to model a system as a filter,
> > in the sense that the input-output is described by a convolution,
> > you are already implicitly assuming that the system is linear and
> > time-invariant.  Do you think that this is the case?  Just wondering
> > out loud, since you didn't explain this part in your original post.
>
> > Julius
>
> If I could I would feed white noise into the system rather than a step
> and take the power spectral density of the output -and average of
> course over time. Assuming minimum phase you could get the transfer
> function of the system. All assuming it is approx linear I suppose
> which giving it is biological it most probably is not.

sheiney wrote:
> 
> Thanks for your responses.
> 
> I had hoped that the system would be "linear enough," but this seems
> to be turning out to not be the case.  In a way, that makes it more
> interesting :-)  The story is actually a little more complicated than
> I initially let on in that I don't actually have total control over
> the input to the system.  The "input" that I have been referring to is
> actually a behavioral output that may be getting fed into the neuron
> through a collateral brain pathway.  It's somewhat complex, which is
> why I didn't explain the problem in this way initially, but what I'm
> actually looking for is a correlation between the behavioral output
> and the response of the neuron.  There seems to be a high correlation
> between the behavior and the neuron in some respects, but the dynamics
> of the behavior and the neuron response are different, which is why I
> thought trying to model the neuron as a filter of the
> "input" (behavior) might be fruitful.
> 
> Despite not having total control of the input to the neuron, I can
> control the behavior in some ways.  I can make it a "step" of
> different amplitudes or I can make it sinusoidal (within a limited
> frequency range).  I can also probably do some arbitrary waveforms.
> However, white noise wouldn't be possible because of the limited
> bandwidth of the behavior.  Accordingly, the "step" isn't really a
> true step in that it takes about 50 msec to get to the new level.  But
> this point is probably moot if the neuron isn't linear, which is how
> things are looking.
> 
> Jim, you mentioned that even if the system isn't linear it could
> possibly still be simple to model.  How might I go about determining
> whether this is the case?

First of all I'm not completely convinced that you are inputting a step
and getting a response from that simply because you say that's what your
doing. But for the purposes of this discussion we will assume that is
what is going on.

	As I said before what you have already done is all you need to do to
extract the frequency response of the system and model it as a
convolution process __if it was linear__. So if it was linear the task
would be dead simple.

	There are many non-linear systems that are also simple. For instance
the ABS() function is not linear but would be pretty easy to discover if
that was what your system looked like. But there are an infinity of
possible non-linear systems. So you are going to need a lot more data.

	As I said before try different amplitude steps as input. You already
know that if you scale the input by -1 the output does not scale
proportionally. That pretty much tells you it is not linear. The
saturation you mentioned also suggest it is not linear. But it still is
possible that if you keep the input signal to within a certain narrow
range of amplitudes it may behave in a linear fashion within that range.
For instance, the ABS function is perfectly linear if you only feed it
positive valued data.

-jim


> 
> shane
> 
> On Jul 22, 12:09 am, gyansor...@gmail.com wrote:
> > On Jul 22, 11:25 am, julius <juli...@gmail.com> wrote:
> >
> >
> >
> > > On Jul 20, 7:11 pm, shei...@gmail.com wrote:
> >
> > > > Hi,
> >
> > > > I'm a biologist so I don't have much experience designing filters, but
> > > > I think I need to apply a filter to some time series data in order to
> > > > model a biological system.
> >
> > > > The problem:
> > > > I know the step response of the system and I need to design a filter
> > > > based on this.  The best way I can describe the step response is that
> > > > it has a logarithmic-like rise that saturates.  Based on my cursory
> > > > understanding of signal processing, this makes me think that I need a
> > > > non-linear phase filter (since the step response is not symmetric).
> > > > Also, because I'm trying to model a biological system it's important
> > > > to use a casual filter.  To add some more complexity, the system has
> > > > different step responses, depending on the polarity of the step.  The
> > > > general shape of the curve is the same, but the time constants are
> > > > different.  So for instance, the time constant is 230 msec for
> > > > positive steps, 80 msec for negative.
> >
> > > [snip]
> >
> > > Shane,
> >
> > > To back off a bit, when you are trying to model a system as a filter,
> > > in the sense that the input-output is described by a convolution,
> > > you are already implicitly assuming that the system is linear and
> > > time-invariant.  Do you think that this is the case?  Just wondering
> > > out loud, since you didn't explain this part in your original post.
> >
> > > Julius
> >
> > If I could I would feed white noise into the system rather than a step
> > and take the power spectral density of the output -and average of
> > course over time. Assuming minimum phase you could get the transfer
> > function of the system. All assuming it is approx linear I suppose
> > which giving it is biological it most probably is not.

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Jim, I absolutely agree that, strictly speaking, I'm not inputting a
step and getting a response.  But I thought what I'm doing
approximates the act enough that I can get some useful information for
designing a filter to mimic the neuron--if it's linear.  The fact that
it appears to be non-linear complicates things, but I don't think the
correct approach for me at this point is to only work within the
linear range because the real system operates in the non-linear range
as well.

I guess I'll just have to go back to the drawing board....

Thanks for your insight.

shane

On Jul 22, 6:55 am, jim <"sjedgingN0sp"@m...@mwt.net> wrote:
> sheiney wrote:
>
> > Thanks for your responses.
>
> > I had hoped that the system would be "linear enough," but this seems
> > to be turning out to not be the case.  In a way, that makes it more
> > interesting :-)  The story is actually a little more complicated than
> > I initially let on in that I don't actually have total control over
> > the input to the system.  The "input" that I have been referring to is
> > actually a behavioral output that may be getting fed into the neuron
> > through a collateral brain pathway.  It's somewhat complex, which is
> > why I didn't explain the problem in this way initially, but what I'm
> > actually looking for is a correlation between the behavioral output
> > and the response of the neuron.  There seems to be a high correlation
> > between the behavior and the neuron in some respects, but the dynamics
> > of the behavior and the neuron response are different, which is why I
> > thought trying to model the neuron as a filter of the
> > "input" (behavior) might be fruitful.
>
> > Despite not having total control of the input to the neuron, I can
> > control the behavior in some ways.  I can make it a "step" of
> > different amplitudes or I can make it sinusoidal (within a limited
> > frequency range).  I can also probably do some arbitrary waveforms.
> > However, white noise wouldn't be possible because of the limited
> > bandwidth of the behavior.  Accordingly, the "step" isn't really a
> > true step in that it takes about 50 msec to get to the new level.  But
> > this point is probably moot if the neuron isn't linear, which is how
> > things are looking.
>
> > Jim, you mentioned that even if the system isn't linear it could
> > possibly still be simple to model.  How might I go about determining
> > whether this is the case?
>
> First of all I'm not completely convinced that you are inputting a step
> and getting a response from that simply because you say that's what your
> doing. But for the purposes of this discussion we will assume that is
> what is going on.
>
>         As I said before what you have already done is all you need to do to
> extract the frequency response of the system and model it as a
> convolution process __if it was linear__. So if it was linear the task
> would be dead simple.
>
>         There are many non-linear systems that are also simple. For instance
> the ABS() function is not linear but would be pretty easy to discover if
> that was what your system looked like. But there are an infinity of
> possible non-linear systems. So you are going to need a lot more data.
>
>         As I said before try different amplitude steps as input. You already
> know that if you scale the input by -1 the output does not scale
> proportionally. That pretty much tells you it is not linear. The
> saturation you mentioned also suggest it is not linear. But it still is
> possible that if you keep the input signal to within a certain narrow
> range of amplitudes it may behave in a linear fashion within that range.
> For instance, the ABS function is perfectly linear if you only feed it
> positive valued data.
>
> -jim
>
>
>
>
>
> > shane
>
> > On Jul 22, 12:09 am, gyansor...@gmail.com wrote:
> > > On Jul 22, 11:25 am, julius <juli...@gmail.com> wrote:
>
> > > > On Jul 20, 7:11 pm, shei...@gmail.com wrote:
>
> > > > > Hi,
>
> > > > > I'm a biologist so I don't have much experience designing filters, but
> > > > > I think I need to apply a filter to some time series data in order to
> > > > > model a biological system.
>
> > > > > The problem:
> > > > > I know the step response of the system and I need to design a filter
> > > > > based on this.  The best way I can describe the step response is that
> > > > > it has a logarithmic-like rise that saturates.  Based on my cursory
> > > > > understanding of signal processing, this makes me think that I need a
> > > > > non-linear phase filter (since the step response is not symmetric).
> > > > > Also, because I'm trying to model a biological system it's important
> > > > > to use a casual filter.  To add some more complexity, the system has
> > > > > different step responses, depending on the polarity of the step.  The
> > > > > general shape of the curve is the same, but the time constants are
> > > > > different.  So for instance, the time constant is 230 msec for
> > > > > positive steps, 80 msec for negative.
>
> > > > [snip]
>
> > > > Shane,
>
> > > > To back off a bit, when you are trying to model a system as a filter,
> > > > in the sense that the input-output is described by a convolution,
> > > > you are already implicitly assuming that the system is linear and
> > > > time-invariant.  Do you think that this is the case?  Just wondering
> > > > out loud, since you didn't explain this part in your original post.
>
> > > > Julius
>
> > > If I could I would feed white noise into the system rather than a step
> > > and take the power spectral density of the output -and average of
> > > course over time. Assuming minimum phase you could get the transfer
> > > function of the system. All assuming it is approx linear I suppose
> > > which giving it is biological it most probably is not.
>
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On Jul 22, 12:09 am, gyansor...@gmail.com wrote:
> On Jul 22, 11:25 am, julius <juli...@gmail.com> wrote:
>
>
>
> > On Jul 20, 7:11 pm, shei...@gmail.com wrote:
>
> > > Hi,
>
> > > I'm a biologist so I don't have much experience designing filters, but
> > > I think I need to apply a filter to some time series data in order to
> > > model a biological system.
>
> > > The problem:
> > > I know the step response of the system and I need to design a filter
> > > based on this.  The best way I can describe the step response is that
> > > it has a logarithmic-like rise that saturates.  Based on my cursory
> > > understanding of signal processing, this makes me think that I need a
> > > non-linear phase filter (since the step response is not symmetric).
> > > Also, because I'm trying to model a biological system it's important
> > > to use a casual filter.  To add some more complexity, the system has
> > > different step responses, depending on the polarity of the step.  The
> > > general shape of the curve is the same, but the time constants are
> > > different.  So for instance, the time constant is 230 msec for
> > > positive steps, 80 msec for negative.
>
> > [snip]
>
> > Shane,
>
> > To back off a bit, when you are trying to model a system as a filter,
> > in the sense that the input-output is described by a convolution,
> > you are already implicitly assuming that the system is linear and
> > time-invariant.  Do you think that this is the case?  Just wondering
> > out loud, since you didn't explain this part in your original post.
>
> > Julius
>
> If I could I would feed white noise into the system rather than a step
> and take the power spectral density of the output -and average of
> course over time. Assuming minimum phase you could get the transfer
> function of the system. All assuming it is approx linear I suppose
> which giving it is biological it most probably is not.

Yep, that approach would be ok if the system was linear and time-
invariant in the first place.   In fact, it is sufficient to give a
signal
that is white in first-order, not second-order, to get a good
estimate.

Many people have worked on a model for biological systems,
but they are almost never purely linear, time-invariant.

Julius