| Author |
Message |
renaudin
Guest
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 Posted:
Mon Dec 19, 2005 5:16 pm Post subject:
How to perform efficient sampling |
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Why use multiple sampling rates? The most important reason is fo
efficiency of calculation and/or memory. But what is the lowest samplin
rate possible? Well, the Nyquist theorem tells us that the sampling rat
must be at least twice the bandwidth of the signal. Therefore, for maximu
efficiency, you would like to do DSP processing at a rate which is a smal
multiple of the signal bandwidth.
Infact I have an oversampled signal and I want to efficiently decimate i
to come to the Nyquist sampling rate.
The problem is matching the sampling rate to the bandwidth of the signa
at each stage of processing?
One hint is the use of Bernstein Inequality, which is applicable for
sinosoid.
|d(x)/dt|<= 2*pi*A*f_max(i).................(1)
In expression-1, 'A' is amplitude dynamics of the oversampled signal. Th
term on left hand side is the slope of the signal and f_max(i) is th
bandwidth of signal at one stage.
Thanks for the ideas!
renaudin |
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Bhaskar Thiagarajan
Guest
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| Posted:
Mon Dec 19, 2005 11:35 pm Post subject:
Re: How to perform efficient sampling |
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"renaudin" <alsaeed86@gmail.com> wrote in message
news:v5SdnccdxoU1eTveRVn-sg@giganews.com...
| Quote: | Why use multiple sampling rates? The most important reason is for
efficiency of calculation and/or memory. But what is the lowest sampling
rate possible? Well, the Nyquist theorem tells us that the sampling rate
must be at least twice the bandwidth of the signal. Therefore, for maximum
efficiency, you would like to do DSP processing at a rate which is a small
multiple of the signal bandwidth.
Infact I have an oversampled signal and I want to efficiently decimate it
to come to the Nyquist sampling rate.
The problem is matching the sampling rate to the bandwidth of the signal
at each stage of processing?
One hint is the use of Bernstein Inequality, which is applicable for a
sinosoid.
|d(x)/dt|<= 2*pi*A*f_max(i).................(1)
In expression-1, 'A' is amplitude dynamics of the oversampled signal. The
term on left hand side is the slope of the signal and f_max(i) is the
bandwidth of signal at one stage.
Thanks for the ideas!
renaudin
|
Hi, I'm sorry but I didn't catch the question in your post - seems like you
were making statements.
If you are wondering why oversample, here are a few reasons
- your hardware used for sampling is not flexible enough to change sample
rates to match your needs.
- it is desirable to do some oversampling to allow for an easier anti-alias
filter ahead of the ADC
- oversampling and decimation in the digital domain allows for improvement
in the SNR of the signal.
Cheers
Bhaskar |
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Fred Marshall
Guest
|
| Posted:
Tue Dec 20, 2005 1:16 am Post subject:
Re: How to perform efficient sampling |
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"renaudin" <alsaeed86@gmail.com> wrote in message
news:v5SdnccdxoU1eTveRVn-sg@giganews.com...
| Quote: | Why use multiple sampling rates? The most important reason is for
efficiency of calculation and/or memory. But what is the lowest sampling
rate possible? Well, the Nyquist theorem tells us that the sampling rate
must be at least twice the bandwidth of the signal. Therefore, for maximum
efficiency, you would like to do DSP processing at a rate which is a small
multiple of the signal bandwidth.
Infact I have an oversampled signal and I want to efficiently decimate it
to come to the Nyquist sampling rate.
The problem is matching the sampling rate to the bandwidth of the signal
at each stage of processing?
One hint is the use of Bernstein Inequality, which is applicable for a
sinosoid.
|d(x)/dt|<= 2*pi*A*f_max(i).................(1)
In expression-1, 'A' is amplitude dynamics of the oversampled signal. The
term on left hand side is the slope of the signal and f_max(i) is the
bandwidth of signal at one stage.
|
Generally the problem is that you don't know "A" or "f" or that the signal
is a sinusoid - for which the expression applies. It won't work for a
composite signal. For example, what if there are 3 sinusoids of similar
frequency all with amplitude A. That could look the same as a single
sinusoid of amplitude A at 3x the frequency - at a point where the maximum
slopes of the 3 sinusoids are aligned.
But, if you know the dynamic range of the signal then you might imply
something from the maximum slope I guess - because the maximum composite
amplitude is known. I don't really know.
As you said:
The problem is matching the sampling rate to the bandwidth of the signal at
each stage of processing.
Assuming that the signal is oversampled to begin with there are a couple of
approaches you might take in reducing the sample rate:
1) Check the effective bandwidth with a Fourier Transform and go from there.
2) Lowpass filter the data prior to decimation or as part of a normal
decimation process.
Decimation by a factor of 2 might look like this:
Lowpass filter to something below fs/4. Decimate by 2. Result, bandwidth
less than the *new* fs/2. Look at half-band filters for this purpose. Only
compute the outputs at the new, lower, sample rate.
Fred |
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renaudin
Guest
|
| Posted:
Thu Dec 22, 2005 4:40 pm Post subject:
Re: How to perform efficient sampling |
|
|
| Quote: |
"renaudin" <alsaeed86@gmail.com> wrote in message
news:v5SdnccdxoU1eTveRVn-sg@giganews.com...
Why use multiple sampling rates? The most important reason is for
efficiency of calculation and/or memory. But what is the lowes
sampling
rate possible? Well, the Nyquist theorem tells us that the samplin
rate
must be at least twice the bandwidth of the signal. Therefore, fo
maximum
efficiency, you would like to do DSP processing at a rate which is
small
multiple of the signal bandwidth.
Infact I have an oversampled signal and I want to efficiently decimat
it
to come to the Nyquist sampling rate.
The problem is matching the sampling rate to the bandwidth of th
signal
at each stage of processing?
One hint is the use of Bernstein Inequality, which is applicable for a
sinosoid.
|d(x)/dt|<= 2*pi*A*f_max(i).................(1)
In expression-1, 'A' is amplitude dynamics of the oversampled signal
The
term on left hand side is the slope of the signal and f_max(i) is the
bandwidth of signal at one stage.
Generally the problem is that you don't know "A" or "f" or that th
signal
is a sinusoid - for which the expression applies. It won't work for a
composite signal. For example, what if there are 3 sinusoids of simila
frequency all with amplitude A. That could look the same as a single
sinusoid of amplitude A at 3x the frequency - at a point where th
maximum
slopes of the 3 sinusoids are aligned.
But, if you know the dynamic range of the signal then you might imply
something from the maximum slope I guess - because the maximum composit
amplitude is known. I don't really know.
As you said:
The problem is matching the sampling rate to the bandwidth of the signa
at
each stage of processing.
Assuming that the signal is oversampled to begin with there are a coupl
of
approaches you might take in reducing the sample rate:
1) Check the effective bandwidth with a Fourier Transform and go fro
there.
2) Lowpass filter the data prior to decimation or as part of a normal
decimation process.
Decimation by a factor of 2 might look like this:
Lowpass filter to something below fs/4. Decimate by 2. Result
bandwidth
less than the *new* fs/2. Look at half-band filters for this purpose.
Only
compute the outputs at the new, lower, sample rate.
Fred
************************************************************************** |
Thanks for the ideas,
1. We can find out the effective Bandwidth with a Fourier Transform bu
this methode requires a lot of computation.
2.Lowpass filter the data prior to decimation process will change it
natural Bandwidth, which I donot want to be change.
** I am Searching for a simple and efficient methode to calculate/estimat
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
Renaudin |
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|
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Guest
|
| Posted:
Thu Dec 22, 2005 4:52 pm Post subject:
Re: How to perform efficient sampling |
|
|
renaudin wrote:
....
| Quote: | 1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
|
I didn't understand your orginial question. It seems now that you have
a signal which you think is oversampled, but you don't know by how
much.
| Quote: | ** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
|
An FFT-based approach wouldn't be the worst idea for this. Since you
don't know to what frequency your signal is bandlimited, you need some
sort of filter bank to estimate the energy of high frequency bands of
your signal. FFT would be an efficient way to compute this. Depending
on the required accuracy of the bandwidth estimate, a bunch of IIR
bandpass filters could be cheaper.
Regards,
Andor |
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|
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Jerry Avins
Guest
|
| Posted:
Thu Dec 22, 2005 5:16 pm Post subject:
Re: How to perform efficient sampling |
|
|
abariska@student.ethz.ch wrote:
| Quote: | renaudin wrote:
...
1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
I didn't understand your orginial question. It seems now that you have
a signal which you think is oversampled, but you don't know by how
much.
** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
An FFT-based approach wouldn't be the worst idea for this. Since you
don't know to what frequency your signal is bandlimited, you need some
sort of filter bank to estimate the energy of high frequency bands of
your signal. FFT would be an efficient way to compute this. Depending
on the required accuracy of the bandwidth estimate, a bunch of IIR
bandpass filters could be cheaper.
|
The /potential/ bandwidth of the signal is half the sample rate. How
much is gained by knowing the actual bandwidth *at a particular time*?
Analyzing the signal source is the only way to know by how much the
maximum possible bandwidth is less than the potential bandwidth.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Michel Rouzic
Guest
|
| Posted:
Fri Dec 23, 2005 1:17 am Post subject:
Re: How to perform efficient sampling |
|
|
Michel Rouzic wrote:
| Quote: | Define a trigger amount of data you can
do without (like for example 1%, however I wouldn't know how to
determine that with a sound)
|
OK, i think I know, but i'm not sure if it would be valid, and i'd risk
doin that only in the polar form with the magnitude part.
Calculate the sum of all the samples in the magnitude part, and then
count down from the top until the sum of the samples you went through
divided by the sum of all the magnitude samples equals the trigger
percentage |
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Michel Rouzic
Guest
|
| Posted:
Fri Dec 23, 2005 1:17 am Post subject:
Re: How to perform efficient sampling |
|
|
renaudin wrote:
| Quote: |
"renaudin" <alsaeed86@gmail.com> wrote in message
news:v5SdnccdxoU1eTveRVn-sg@giganews.com...
Why use multiple sampling rates? The most important reason is for
efficiency of calculation and/or memory. But what is the lowest
sampling
rate possible? Well, the Nyquist theorem tells us that the sampling
rate
must be at least twice the bandwidth of the signal. Therefore, for
maximum
efficiency, you would like to do DSP processing at a rate which is a
small
multiple of the signal bandwidth.
Infact I have an oversampled signal and I want to efficiently decimate
it
to come to the Nyquist sampling rate.
The problem is matching the sampling rate to the bandwidth of the
signal
at each stage of processing?
One hint is the use of Bernstein Inequality, which is applicable for a
sinosoid.
|d(x)/dt|<= 2*pi*A*f_max(i).................(1)
In expression-1, 'A' is amplitude dynamics of the oversampled signal.
The
term on left hand side is the slope of the signal and f_max(i) is the
bandwidth of signal at one stage.
Generally the problem is that you don't know "A" or "f" or that the
signal
is a sinusoid - for which the expression applies. It won't work for a
composite signal. For example, what if there are 3 sinusoids of similar
frequency all with amplitude A. That could look the same as a single
sinusoid of amplitude A at 3x the frequency - at a point where the
maximum
slopes of the 3 sinusoids are aligned.
But, if you know the dynamic range of the signal then you might imply
something from the maximum slope I guess - because the maximum composite
amplitude is known. I don't really know.
As you said:
The problem is matching the sampling rate to the bandwidth of the signal
at
each stage of processing.
Assuming that the signal is oversampled to begin with there are a couple
of
approaches you might take in reducing the sample rate:
1) Check the effective bandwidth with a Fourier Transform and go from
there.
2) Lowpass filter the data prior to decimation or as part of a normal
decimation process.
Decimation by a factor of 2 might look like this:
Lowpass filter to something below fs/4. Decimate by 2. Result,
bandwidth
less than the *new* fs/2. Look at half-band filters for this purpose.
Only
compute the outputs at the new, lower, sample rate.
Fred
**************************************************************************
Thanks for the ideas,
1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
2.Lowpass filter the data prior to decimation process will change its
natural Bandwidth, which I donot want to be change.
** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
Renaudin
|
(Disclaimer : I'm a newbie)
If I was you, i'd go for a FFT. Define a trigger amount of data you can
do without (like for example 1%, however I wouldn't know how to
determine that with a sound), and look for the real and imaginary parts
from the top (i mean the highest frequencies) until you went through
the trigger amount of data you can get rid of. then, just cut these
parts and perform an Inverse FFT (and don't forget to calculate whats
the new sampling frequency) |
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Fred Marshall
Guest
|
| Posted:
Fri Dec 23, 2005 9:15 am Post subject:
Re: How to perform efficient sampling |
|
|
"renaudin" <alsaeed86@gmail.com> wrote in message
news:y_-dnU6TlqAYHzfeRVn-jg@giganews.com...
| Quote: | 1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
2.Lowpass filter the data prior to decimation process will change its
natural Bandwidth, which I donot want to be change.
** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
Renaudin
|
Well, the lowpass filter in (2) should not change the signal much. If it
does then you have no business decimating - unless aliasing is OK for you.
In view of how particular your application seems to be, I'd imagine aliasing
is not OK.
Maybe the way to proceed is to calculate the Fourier coefficients from the
high end down and stop when the magnitude becomes "important". Goertzel
algorithm?
Fred |
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Jerry Avins
Guest
|
| Posted:
Fri Dec 23, 2005 5:15 pm Post subject:
Re: How to perform efficient sampling |
|
|
abariska@student.ethz.ch wrote:
...
| Quote: | I think the OP is faced with a signal with varying bandwidth, otherwise
a frame-by-frame analysis makes no sense.
|
Pity the poor receiver! (And think how much more might be gained by
choosing the sample rate line by line.)
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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|
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Guest
|
| Posted:
Fri Dec 23, 2005 5:15 pm Post subject:
Re: How to perform efficient sampling |
|
|
Jerry Avins wrote:
| Quote: | abariska@student.ethz.ch wrote:
renaudin wrote:
...
1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
I didn't understand your orginial question. It seems now that you have
a signal which you think is oversampled, but you don't know by how
much.
** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
An FFT-based approach wouldn't be the worst idea for this. Since you
don't know to what frequency your signal is bandlimited, you need some
sort of filter bank to estimate the energy of high frequency bands of
your signal. FFT would be an efficient way to compute this. Depending
on the required accuracy of the bandwidth estimate, a bunch of IIR
bandpass filters could be cheaper.
The /potential/ bandwidth of the signal is half the sample rate. How
much is gained by knowing the actual bandwidth *at a particular time*?
|
I think that the OP wants to reduce the data rate from a (highly?)
oversampled signal. It is my reading of his question that he wants to
do this on a frame by frame basis, determine the maximum bandwidth for
each frame, and adjust the sample rate accordingly.
| Quote: | Analyzing the signal source is the only way to know by how much the
maximum possible bandwidth is less than the potential bandwidth.
|
I think the OP is faced with a signal with varying bandwidth, otherwise
a frame-by-frame analysis makes no sense.
Regards,
Andor |
|
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|
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John Herman
Guest
|
| Posted:
Sat Dec 24, 2005 11:47 pm Post subject:
Re: How to perform efficient sampling |
|
|
In article <y_-dnU6TlqAYHzfeRVn-jg@giganews.com>, "renaudin" <alsaeed86@gmail.com> wrote:
| Quote: | **************************************************************************
Thanks for the ideas,
1. We can find out the effective Bandwidth with a Fourier Transform but
this methode requires a lot of computation.
2.Lowpass filter the data prior to decimation process will change its
natural Bandwidth, which I donot want to be change.
** I am Searching for a simple and efficient methode to calculate/estimate
the natural Bandwidth of a signal.
Looking forward for the discussion and ideas.
Renaudin
|
Estimating the signal bandwidth is very hard to do in realtime. It is nearly
impossible unless the signal to noise ratio is high. In any case, you would
have to design the system for the maximum bandwidth.
If you were going to estimate the signal bandwidth, you would likely have to
depend on halfband filters and power detectors to determine the bandwidth.
With a series of halfband filters, you could do a binary search to determine
the bandwidth of the signal. This would allow you to decimate by one-half,
one-quarter, one-eighth, ... as appropriate for your signal bandwidth. |
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