bandpass sampling question

Hi,

I have a bandpass signal centered around 40kHz. It's pretty narrow in
bandwidth, around 1ms in duration. I'm bandpass-sampling this signal
by fs = 38kHz, and hence mixing it down to 2kHz---for the time being
I'm experimenting with this. Now this is where I'm getting a bit
confused. When I view the acquired waveform, I see two roughly cycles
within an envelop that spans approximately 400 points. I know that the
two cycles should correspond to a 2kHz sinusoid within the 1ms
envelop. However, what about the 400 points, I don't know exactly how
to interpret this.

From observing the waveform, I also noticed pretty visible quantized
values that change every ~14, ~15 samples. By empirically removing
these redundant values, my final waveform now looks quite sooth and
only extends over ~35 points. I don't know exactly what to make out of
all this.

My two questions, therefore, are:
- why 400 points when theoretically the signal is only 1ms long
- what about the quantization in the waveform. I know according to the
bandpass sampling theorem, a filter should be used on the resultant
signal to extract the desired image from nearby replicas.

I would be most grateful for any assistance on this.

Regards,
Momo

On Apr 9, 7:21 am, momo.lo...@googlemail.com wrote:
> Hi,
>
> I have a bandpass signal centered around 40kHz. It's pretty narrow in
> bandwidth, around 1ms in duration. I'm bandpass-sampling this signal
> by fs = 38kHz, and hence mixing it down to 2kHz---for the time being
> I'm experimenting with this. Now this is where I'm getting a bit
> confused. When I view the acquired waveform, I see two roughly cycles
> within an envelop that spans approximately 400 points. I know that the
> two cycles should correspond to a 2kHz sinusoid within the 1ms
> envelop. However, what about the 400 points, I don't know exactly how
> to interpret this.
>
> From observing the waveform, I also noticed pretty visible quantized
> values that change every ~14, ~15 samples. By empirically removing
> these redundant values, my final waveform now looks quite sooth and
> only extends over ~35 points. I don't know exactly what to make out of
> all this.
>
> My two questions, therefore, are:
> - why 400 points when theoretically the signal is only 1ms long
> - what about the quantization in the waveform. I know according to the
> bandpass sampling theorem, a filter should be used on the resultant
> signal to extract the desired image from nearby replicas.
>
> I would be most grateful for any assistance on this.
>
> Regards,
> Momo

It sounds like your data acquisition logic is giving you repeated
samples. If the 1 ms pulse was being stretched out 10X by a narrow
filter, it would not be stairstepped as you describe.

John

On Apr 9, 7:21�am, momo.lo...@googlemail.com wrote:
> Hi,
>
> I have a bandpass signal centered around 40kHz. It's pretty narrow in
> bandwidth, around 1ms in duration. I'm bandpass-sampling this signal
> by fs = 38kHz, and hence mixing it down to 2kHz---for the time being
> I'm experimenting with this. Now this is where I'm getting a bit
> confused. When I view the acquired waveform, I see two roughly cycles
> within an envelop that spans approximately 400 points. I know that the
> two cycles should correspond to a 2kHz sinusoid within the 1ms
> envelop. However, what about the 400 points, I don't know exactly how
> to interpret this.
>
> From observing the waveform, I also noticed pretty visible quantized
> values that change every ~14, ~15 samples. By empirically removing
> these redundant values, my final waveform now looks quite sooth and
> only extends over ~35 points. I don't know exactly what to make out of
> all this.
>
> My two questions, therefore, are:
> - why 400 points when theoretically the signal is only 1ms long
> - what about the quantization in the waveform. I know according to the
> bandpass sampling theorem, a filter should be used on the resultant
> signal to extract the desired image from nearby replicas.
>
> I would be most grateful for any assistance on this.
>
> Regards,
> Momo

you say your signal is CENTERED at 40 kHz, but does it have components
near 38 kHz that would give you low frequency energy after sub-
sampling.

Mark

<momo.lolah@googlemail.com> wrote in message 
news:4ec86a8f-b51f-4f1b-99b3-15c50ffd18ac@m44g2000hsc.googlegroups.com...
> Hi,
>
> I have a bandpass signal centered around 40kHz. It's pretty narrow in
> bandwidth, around 1ms in duration. I'm bandpass-sampling this signal
> by fs = 38kHz, and hence mixing it down to 2kHz---for the time being
> I'm experimenting with this. Now this is where I'm getting a bit
> confused. When I view the acquired waveform, I see two roughly cycles
> within an envelop that spans approximately 400 points. I know that the
> two cycles should correspond to a 2kHz sinusoid within the 1ms
> envelop. However, what about the 400 points, I don't know exactly how
> to interpret this.
>
> From observing the waveform, I also noticed pretty visible quantized
> values that change every ~14, ~15 samples. By empirically removing
> these redundant values, my final waveform now looks quite sooth and
> only extends over ~35 points. I don't know exactly what to make out of
> all this.
>
> My two questions, therefore, are:
> - why 400 points when theoretically the signal is only 1ms long
> - what about the quantization in the waveform. I know according to the
> bandpass sampling theorem, a filter should be used on the resultant
> signal to extract the desired image from nearby replicas.
>
> I would be most grateful for any assistance on this.

It's not all that clear what you're doing so I'm going to guess:

1) You have a signal that's not yet sampled.

2) The continuous signal is centered at 40kHz and has a bandwidth of 2kHz.

3) You sample at 38kHz thus creating a new center frequency of 40-38=2kHz 
and a mirror image at -40+38=-2kHz.  So, there is enough guard band around 
zero.

At this stage, the total bandwidth is 6kHz (2kHz BW centered at -2kHz starts 
at -3kHz and 2kHz bandwith centered at 2kHz ends at 3kHz.  So, you'd need a 
sample rate that's at least 12kHz. With 38kHz, that seems OK.

Now let's talk a bit more specifically about the signal:

The signal is a sinusoid at 40kHz and the duration is 1msec so there should 
be 40 cycles within that 1msec.
Actually, cutting off a sinusoid that abruptly will make the bandwidth 
larger than the 1kHz "clump" of energy implied by the 1msec duration - that 
only accounts for a part of the bandwidth.  One might easily take the 
bandwidth to be 10X that unless the "pulse" is shaped / windowed.

When you sample at 38kHz, the 40kHz signal is captured such that the result 
looks like a 2kHz sinusoid sampled at 38kHz and with the 1msec duration it 
will have 38 samples within that 1msec.  It's not possible to tell the 
difference between the 40kHz signal and a 2kHz signal after sampling.

How you get 400 samples out of this is most unclear.  You've not said *how 
many* samples are taken.

400 samples at 40kHz has a duration of 10msec.
2 cycles over 10msec has a frequency of 200Hz.

It looks like something is wrong with the numbers here....

Fred

Thanks a lot all. I'm leaning now to the possibility that the data
acquisition logic is acting funny on me. Until now, I had been totally
dismissing this from the realm of possibilities. Now I'll have to dig
into this and probe the code carefully---Thanks John.

I'll be reporting on this soon.

Many thanks,
Momo

I've now managed to spot the problem in the acquisition code. Not
gonna trouble you with the details really. It was just to do with sync
flags between the main and interrupt processes. I initially wrote
everything with an OS in mind but ended up not using one. The probelm
now is fixed. Thanks for all who replied. And thanks for John again
for pointing out this possibility.

Momo