R help - Oct 2009 - three related time series with different resolutions

I have three time series, x, y, and z, and I want to analyse the
relations between them. However, they have vastly different
resolutions. I am writing to ask for advice on how to handle this
situation in R.

x is a stimulus, and y and z are responses.

x is a rectangular pulse 4 sec long. Its onset and offset are known
with sub-millisecond precision. The onset varies irregularly -- it
doesn't fall on neat 1/2 sec or sec boundaries for example.

y is a sampled continuous waveform. It is highly noisy, and it is
actually well represented by samples 1/2 sec apart or so.

z is a very short pulse -- perhaps 5 ms long -- occurring at irregular times.

I have problems with how to represent these waveforms at the input
stage (during data collection) and at the analysis stage. If I want to
represent x and z with the sort of precision I'd like, I'd have to
sample every ms or so. But:
- that is massive overkill for y, because it is noisy. I will have
maybe 500 times as many pts as I require! That makes for large data
files, for no good reason.
- the representations for x and z are about 99% zeros. Again, wasteful
for storage
- the analysis will be awkward and slow because of the huge number of pts

If I sample at a rate of every 1/2 sec, z may be not detected at all,
and the edges of x are represented very poorly.

I could just save y as a separate file, with values sampled every 1/2
sec, save x as a file containing onset and offset times, and save z as
the times of each impulse. All three files have different lengths. If
I save this way it is awkward keeping track of the three files for
each run, and I'm still left with the problem of analysing them. In my
mind they are actually three continuous waveforms, and my
simple-minded way of analysing would be to create digitised waveform
versions of all three (on some fine grain). If I do that I still have
the problem of zillions of useless points clogging RAM.

What do I want from the analysis?
I want the average waveform for y that occurs for 30 sec after each x
pulse, and the average waveform for z that occurs for 30 sec after
each x pulse. The average waveform for y surrounding each z (maybe 30
sec before and 10 sec after) would also be useful.

Thanks very much for any suggestions about representation for data
collection and analysis, and for data analysis methods (which will
depend on the data representation).

Bill

PS I think one way to get the average waveforms I want from the
analysis is using cross-correlation, but again the multiple scale
problem is present.

On Wed, Oct 21, 2009 at 9:56 AM, William Simpson
<william.a.simpson at gmail.com> wrote:
> I have three time series, x, y, and z, and I want to analyse the
> relations between them. However, they have vastly different
> resolutions. I am writing to ask for advice on how to handle this
> situation in R.
>
> x is a stimulus, and y and z are responses.
>
> x is a rectangular pulse 4 sec long. Its onset and offset are known
> with sub-millisecond precision. The onset varies irregularly -- it
> doesn't fall on neat 1/2 sec or sec boundaries for example.
>
> y is a sampled continuous waveform. It is highly noisy, and it is
> actually well represented by samples 1/2 sec apart or so.
>
> z is a very short pulse -- perhaps 5 ms long -- occurring at irregular
times.
>
> I have problems with how to represent these waveforms at the input
> stage (during data collection) and at the analysis stage. If I want to
> represent x and z with the sort of precision I'd like, I'd have to
> sample every ms or so. But:
> - that is massive overkill for y, because it is noisy. I will have
> maybe 500 times as many pts as I require! That makes for large data
> files, for no good reason.
> - the representations for x and z are about 99% zeros. Again, wasteful
> for storage
> - the analysis will be awkward and slow because of the huge number of pts
>
> If I sample at a rate of every 1/2 sec, z may be not detected at all,
> and the edges of x are represented very poorly.
>
> I could just save y as a separate file, with values sampled every 1/2
> sec, save x as a file containing onset and offset times, and save z as
> the times of each impulse. All three files have different lengths. If
> I save this way it is awkward keeping track of the three files for
> each run, and I'm still left with the problem of analysing them. In my
> mind they are actually three continuous waveforms, and my
> simple-minded way of analysing would be to create digitised waveform
> versions of all three (on some fine grain). If I do that I still have
> the problem of zillions of useless points clogging RAM.
>
> What do I want from the analysis?
> I want the average waveform for y that occurs for 30 sec after each x
> pulse, and the average waveform for z that occurs for 30 sec after
> each x pulse. The average waveform for y surrounding each z (maybe 30
> sec before and 10 sec after) would also be useful.
>
> Thanks very much for any suggestions about representation for data
> collection and analysis, and for data analysis methods (which will
> depend on the data representation).
>
> Bill
>

I wasn't clear: x and z are pulse *trains* with irregular gaps between
pulses.
>
> x is a rectangular pulse 4 sec long. Its onset and offset are known
> with sub-millisecond precision. The onset varies irregularly -- it
> doesn't fall on neat 1/2 sec or sec boundaries for example.
>
> y is a sampled continuous waveform. It is highly noisy, and it is
> actually well represented by samples 1/2 sec apart or so.
>
> z is a very short pulse -- perhaps 5 ms long -- occurring at irregular
times.