frequency resolution issue

Hi all,I am a newer in DSP. I have a frequency resolution problem, need
your suggestions and comments.

My problem depends on frequency resolution. Basically I need the frequency
resolution around 0.01-0.02 at least to make the error smaller. But my
useful signal is roughly 10s which means the frequency resolution is 0.1Hz,
this is far away from my requirement. Does anybody know if there is method
can solve this issue?

One of my friends suggested me to patch the "good connected signal" from
the original signal to the end of the time series to make the signal very
long. I don't think this will work, but I don't know how to argue with him.
Anybody can give me a theory for this so that I can argue with him.

I also want to try use longer time series to get the frequency fM, then
for the shorter time series I can extract the frequency component for fM.
The problem is there is no frequency from FFT exactly equal to fM. So how
can I extract the component from the shorter time series based on fM
calculated by longer time series. I know we can interpolate by
zero-padding, But I feel I can not extract the exact component from this.

Hope I made my problem clear. Thank you all

On Jul 21, 5:50&#4294967295;pm, "biantai" <wrxd...@gmail.com> wrote:
> Hi all,I am a newer in DSP. I have a frequency resolution problem, need
> your suggestions and comments.
>
> My problem depends on frequency resolution. Basically I need the frequency
> resolution around 0.01-0.02 at least to make the error smaller. But my
> useful signal is roughly 10s which means the frequency resolution is 0.1Hz,
> this is far away from my requirement. Does anybody know if there is method
> can solve this issue?

Frequency resolution depends not only on the length of the
"useful signal" but also on the signal-to-noise ratio.  In the
pure zero noise case, you can get a perfect frequency measurement
with only 3 (non-aliased) sample points. And in a high noise
situation, you may need a lot more data just to determine
whether your signal is present, much less measure its frequency
to even 1 Hz.

There are lots of frequency estimation methods which may work
for signal-to-noise ratios within certain ranges.  I have a big
list of various estimation methods, some of which may or may not
be useful, on one of my web pages:
 http://www.nicholson.com/rhn/dsp.html


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

>On Jul 21, 5:50=A0pm, "biantai" <wrxd...@gmail.com> wrote:
>> Hi all,I am a newer in DSP. I have a frequency resolution problem,
need
>> your suggestions and comments.
>>
>> My problem depends on frequency resolution. Basically I need the
frequenc=
>y
>> resolution around 0.01-0.02 at least to make the error smaller. But my
>> useful signal is roughly 10s which means the frequency resolution is
0.1H=
>z,
>> this is far away from my requirement. Does anybody know if there is
metho=
>d
>> can solve this issue?
>
>Frequency resolution depends not only on the length of the
>"useful signal" but also on the signal-to-noise ratio.  In the
>pure zero noise case, you can get a perfect frequency measurement
>with only 3 (non-aliased) sample points. And in a high noise
>situation, you may need a lot more data just to determine
>whether your signal is present, much less measure its frequency
>to even 1 Hz.
>
>There are lots of frequency estimation methods which may work
>for signal-to-noise ratios within certain ranges.  I have a big
>list of various estimation methods, some of which may or may not
>be useful, on one of my web pages:
> http://www.nicholson.com/rhn/dsp.html
>
>
>IMHO. YMMV.
>--
>rhn A.T nicholson d.0.t C-o-M
>
============
Thank you Ron for your response.
I will check your site to see what method is good for me.
By the way, how do I know signal/noise? 
basically, I measure the wave propagating into ice in a wave tank.
Because I only concern about the beginning part. So there is no
reflection
but the amplitude may change with time and assume only one frequency
generated.

On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
> Hi all,I am a newer in DSP. I have a frequency resolution problem, need
> your suggestions and comments.
>
> My problem depends on frequency resolution. Basically I need the frequency
> resolution around 0.01-0.02 at least to make the error smaller. But my
> useful signal is roughly 10s which means the frequency resolution is 0.1Hz,
> this is far away from my requirement. Does anybody know if there is method
> can solve this issue?

It depends on the exact problem you try to solve. "Resolution" can
mean
two things, either the ability to find the frequeny of *one*
sinusoidal
with high accuracy, or to separate *two* sinusoidals at similar
frequencies.

The available solution methods depend on what you try to do and why.

> One of my friends suggested me to patch the "good connected signal" from
> the original signal to the end of the time series to make the signal very
> long. I don't think this will work, but I don't know how to argue with him.
> Anybody can give me a theory for this so that I can argue with him.

It's an interesting exercise if you try it, but it will not solve
your
problem since you do not introduce new information to the signal.

Try this in matlab:

s=randn(100,1);
stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
hold on
S=[s;s];
stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')

It should be no surprise that you get all the same coefficients
in the extended signal as in the original signal (save a scale
factor). Since you did not add any new information, the 'extra'
coefficients in the spectrum of the extended sequence are 0.

> I also want to try use longer time series to get the frequency fM, then
> for the shorter time series I can extract the frequency component for fM.

So what you *really* want to do is to decode an FM signal?

> The problem is there is no frequency from FFT exactly equal to fM. So how
> can I extract the component from the shorter time series based on fM
> calculated by longer time series. I know we can interpolate by
> zero-padding, But I feel I can not extract the exact component from this.
>
> Hope I made my problem clear. Thank you all

No, you haven't. What do you try to do? Estimate the frequency of
one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?

Rune

>On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
>> Hi all,I am a newer in DSP. I have a frequency resolution problem,
need
>> your suggestions and comments.
>>
>> My problem depends on frequency resolution. Basically I need the
frequency
>> resolution around 0.01-0.02 at least to make the error smaller. But my
>> useful signal is roughly 10s which means the frequency resolution is
0.1Hz,
>> this is far away from my requirement. Does anybody know if there is
method
>> can solve this issue?
>
>It depends on the exact problem you try to solve. "Resolution" can
>mean
>two things, either the ability to find the frequeny of *one*
>sinusoidal
>with high accuracy, or to separate *two* sinusoidals at similar
>frequencies.
>
>The available solution methods depend on what you try to do and why.
>
>> One of my friends suggested me to patch the "good connected signal"
from
>> the original signal to the end of the time series to make the signal
very
>> long. I don't think this will work, but I don't know how to argue with
him.
>> Anybody can give me a theory for this so that I can argue with him.
>
>It's an interesting exercise if you try it, but it will not solve
>your
>problem since you do not introduce new information to the signal.
>
>Try this in matlab:
>
>s=randn(100,1);
>stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
>hold on
>S=[s;s];
>stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')
>
>It should be no surprise that you get all the same coefficients
>in the extended signal as in the original signal (save a scale
>factor). Since you did not add any new information, the 'extra'
>coefficients in the spectrum of the extended sequence are 0.
>
>> I also want to try use longer time series to get the frequency fM,
then
>> for the shorter time series I can extract the frequency component for
fM.
>
>So what you *really* want to do is to decode an FM signal?
>
>> The problem is there is no frequency from FFT exactly equal to fM. So
how
>> can I extract the component from the shorter time series based on fM
>> calculated by longer time series. I know we can interpolate by
>> zero-padding, But I feel I can not extract the exact component from
this.
>>
>> Hope I made my problem clear. Thank you all
>
>No, you haven't. What do you try to do? Estimate the frequency of
>one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?
>
>Rune
>===============
Thank you Rune,
To clarify my problem, I want to estimate accurately the frequency of one
sinusoidal, not separate two sinusoidals because there is only one main
frequency in my signal. My problem is strongly depends on the frequency
resolution, which means small frequency change will introduce big error in
my problem. basically, I need the resolution about 0.01-0.02Hz. 

The wave signal I recorded is about 40-50s. But because it is hard to
separate the reflected wave and incident wave for my situation, I need use
only the beginning part to analysis (7s to 10s). So my second question is
trying get the frequency from the whole signal which give the resolution
about 0.02Hz, then use this frequency(lets say fM) to analysis the
beginning part. Since 7s to 10s signal may not give extact fM component,
how can I extract the fM component from this short period.

Ray

On 22 Jul, 19:11, "biantai" <wrxd...@gmail.com> wrote:
> >On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
> >> Hi all,I am a newer in DSP. I have a frequency resolution problem,
> need
> >> your suggestions and comments.
>
> >> My problem depends on frequency resolution. Basically I need the
> frequency
> >> resolution around 0.01-0.02 at least to make the error smaller. But my
> >> useful signal is roughly 10s which means the frequency resolution is
> 0.1Hz,
> >> this is far away from my requirement. Does anybody know if there is
> method
> >> can solve this issue?
>
> >It depends on the exact problem you try to solve. "Resolution" can
> >mean
> >two things, either the ability to find the frequeny of *one*
> >sinusoidal
> >with high accuracy, or to separate *two* sinusoidals at similar
> >frequencies.
>
> >The available solution methods depend on what you try to do and why.
>
> >> One of my friends suggested me to patch the "good connected signal"
> from
> >> the original signal to the end of the time series to make the signal
> very
> >> long. I don't think this will work, but I don't know how to argue with
> him.
> >> Anybody can give me a theory for this so that I can argue with him.
>
> >It's an interesting exercise if you try it, but it will not solve
> >your
> >problem since you do not introduce new information to the signal.
>
> >Try this in matlab:
>
> >s=randn(100,1);
> >stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
> >hold on
> >S=[s;s];
> >stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')
>
> >It should be no surprise that you get all the same coefficients
> >in the extended signal as in the original signal (save a scale
> >factor). Since you did not add any new information, the 'extra'
> >coefficients in the spectrum of the extended sequence are 0.
>
> >> I also want to try use longer time series to get the frequency fM,
> then
> >> for the shorter time series I can extract the frequency component for
> fM.
>
> >So what you *really* want to do is to decode an FM signal?
>
> >> The problem is there is no frequency from FFT exactly equal to fM. So
> how
> >> can I extract the component from the shorter time series based on fM
> >> calculated by longer time series. I know we can interpolate by
> >> zero-padding, But I feel I can not extract the exact component from
> this.
>
> >> Hope I made my problem clear. Thank you all
>
> >No, you haven't. What do you try to do? Estimate the frequency of
> >one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?
>
> >Rune
> >===============
>
> Thank you Rune,
> To clarify my problem, I want to estimate accurately the frequency of one
> sinusoidal, not separate two sinusoidals because there is only one main
> frequency in my signal. My problem is strongly depends on the frequency
> resolution, which means small frequency change will introduce big error in
> my problem. basically, I need the resolution about 0.01-0.02Hz.

You need 50-100 s of data to get that.

> The wave signal I recorded is about 40-50s. But because it is hard to
> separate the reflected wave and incident wave for my situation, I need use
> only the beginning part to analysis (7s to 10s). So my second question is
> trying get the frequency from the whole signal which give the resolution
> about 0.02Hz, then use this frequency(lets say fM) to analysis the
> beginning part. Since 7s to 10s signal may not give extact fM component,
> how can I extract the fM component from this short period.

What type of signal is this? You talk about 'pulse' and 'reflection'.
Those are usually transients, meaning that frequency estimation
is more or less meaningless since you transmitted the signal
yourself and - presumably - already know what you sent.

Could you please decribe the experiment and application?

Rune

>On 22 Jul, 19:11, "biantai" <wrxd...@gmail.com> wrote:
>> >On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
>> >> Hi all,I am a newer in DSP. I have a frequency resolution problem,
>> need
>> >> your suggestions and comments.
>>
>> >> My problem depends on frequency resolution. Basically I need the
>> frequency
>> >> resolution around 0.01-0.02 at least to make the error smaller. But
my
>> >> useful signal is roughly 10s which means the frequency resolution
is
>> 0.1Hz,
>> >> this is far away from my requirement. Does anybody know if there is
>> method
>> >> can solve this issue?
>>
>> >It depends on the exact problem you try to solve. "Resolution" can
>> >mean
>> >two things, either the ability to find the frequeny of *one*
>> >sinusoidal
>> >with high accuracy, or to separate *two* sinusoidals at similar
>> >frequencies.
>>
>> >The available solution methods depend on what you try to do and why.
>>
>> >> One of my friends suggested me to patch the "good connected signal"
>> from
>> >> the original signal to the end of the time series to make the
signal
>> very
>> >> long. I don't think this will work, but I don't know how to argue
with
>> him.
>> >> Anybody can give me a theory for this so that I can argue with him.
>>
>> >It's an interesting exercise if you try it, but it will not solve
>> >your
>> >problem since you do not introduce new information to the signal.
>>
>> >Try this in matlab:
>>
>> >s=randn(100,1);
>> >stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
>> >hold on
>> >S=[s;s];
>> >stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')
>>
>> >It should be no surprise that you get all the same coefficients
>> >in the extended signal as in the original signal (save a scale
>> >factor). Since you did not add any new information, the 'extra'
>> >coefficients in the spectrum of the extended sequence are 0.
>>
>> >> I also want to try use longer time series to get the frequency fM,
>> then
>> >> for the shorter time series I can extract the frequency component
for
>> fM.
>>
>> >So what you *really* want to do is to decode an FM signal?
>>
>> >> The problem is there is no frequency from FFT exactly equal to fM.
So
>> how
>> >> can I extract the component from the shorter time series based on
fM
>> >> calculated by longer time series. I know we can interpolate by
>> >> zero-padding, But I feel I can not extract the exact component from
>> this.
>>
>> >> Hope I made my problem clear. Thank you all
>>
>> >No, you haven't. What do you try to do? Estimate the frequency of
>> >one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?
>>
>> >Rune
>> >===============
>>
>> Thank you Rune,
>> To clarify my problem, I want to estimate accurately the frequency of
one
>> sinusoidal, not separate two sinusoidals because there is only one
main
>> frequency in my signal. My problem is strongly depends on the
frequency
>> resolution, which means small frequency change will introduce big error
in
>> my problem. basically, I need the resolution about 0.01-0.02Hz.
>
>You need 50-100 s of data to get that.
>
>> The wave signal I recorded is about 40-50s. But because it is hard to
>> separate the reflected wave and incident wave for my situation, I need
use
>> only the beginning part to analysis (7s to 10s). So my second question
is
>> trying get the frequency from the whole signal which give the
resolution
>> about 0.02Hz, then use this frequency(lets say fM) to analysis the
>> beginning part. Since 7s to 10s signal may not give extact fM
component,
>> how can I extract the fM component from this short period.
>
>What type of signal is this? You talk about 'pulse' and 'reflection'.
>Those are usually transients, meaning that frequency estimation
>is more or less meaningless since you transmitted the signal
>yourself and - presumably - already know what you sent.
>
>Could you please decribe the experiment and application?
>
>Rune
>===============================
Rune, I measure the gravity water wave propagating into ice cover in the
lab. The wave will reflect from the beach. Because the wave damps under ice
cover, it is hard to separate the incident wave and reflected wave. For my
analysis, I need use the pure incident wave which means there is no
reflection, I call it the beginning part in my last post. I assume that the
wave paddle only generate one frequency. 

"biantai" <wrxdlut@gmail.com> wrote in message 
news:uumdnXJXkuhWsxjVnZ2dnUVZ_sninZ2d@giganews.com...
> Hi all,I am a newer in DSP. I have a frequency resolution problem, need
> your suggestions and comments.
>
> My problem depends on frequency resolution. Basically I need the frequency
> resolution around 0.01-0.02 at least to make the error smaller. But my
> useful signal is roughly 10s which means the frequency resolution is 
> 0.1Hz,
> this is far away from my requirement. Does anybody know if there is method
> can solve this issue?
>
> One of my friends suggested me to patch the "good connected signal" from
> the original signal to the end of the time series to make the signal very
> long. I don't think this will work, but I don't know how to argue with 
> him.
> Anybody can give me a theory for this so that I can argue with him.
>

Sure.  If you concatenate copies of the signal with itself it will be 
periodic won't it?

If it's periodic, then it's represented by harmonics which are spaced 
exactly the same as the original frequency samples.  Because the splice 
points are likely discontinous, there will be some energy between the 
harmonic samples but that's "noise" to you.  If you were able to capture a 
perfect integer number of periods and then splice those you would generate 
less transient noise at the edges and the interim samples would be closer to 
zero.

I once tried to generate a submarine noise signature using a rather short 
memory (of time length T) that would play in a "loop".  It sounded great 
after I adjusted the length to match the fundamental beats so there was no 
discernible transient.  BUT: No surprise now that I learned its spectrum was 
quite discrete - i.e. made up of lines separated by 1/T.  Same idea .....

Fred 

On 23 Jul, 00:24, "biantai" <wrxd...@gmail.com> wrote:
> >On 22 Jul, 19:11, "biantai" <wrxd...@gmail.com> wrote:
> >> >On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
> >> >> Hi all,I am a newer in DSP. I have a frequency resolution problem,
> >> need
> >> >> your suggestions and comments.
>
> >> >> My problem depends on frequency resolution. Basically I need the
> >> frequency
> >> >> resolution around 0.01-0.02 at least to make the error smaller. But
> my
> >> >> useful signal is roughly 10s which means the frequency resolution
> is
> >> 0.1Hz,
> >> >> this is far away from my requirement. Does anybody know if there is
> >> method
> >> >> can solve this issue?
>
> >> >It depends on the exact problem you try to solve. "Resolution" can
> >> >mean
> >> >two things, either the ability to find the frequeny of *one*
> >> >sinusoidal
> >> >with high accuracy, or to separate *two* sinusoidals at similar
> >> >frequencies.
>
> >> >The available solution methods depend on what you try to do and why.
>
> >> >> One of my friends suggested me to patch the "good connected signal"
> >> from
> >> >> the original signal to the end of the time series to make the
> signal
> >> very
> >> >> long. I don't think this will work, but I don't know how to argue
> with
> >> him.
> >> >> Anybody can give me a theory for this so that I can argue with him.
>
> >> >It's an interesting exercise if you try it, but it will not solve
> >> >your
> >> >problem since you do not introduce new information to the signal.
>
> >> >Try this in matlab:
>
> >> >s=randn(100,1);
> >> >stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
> >> >hold on
> >> >S=[s;s];
> >> >stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')
>
> >> >It should be no surprise that you get all the same coefficients
> >> >in the extended signal as in the original signal (save a scale
> >> >factor). Since you did not add any new information, the 'extra'
> >> >coefficients in the spectrum of the extended sequence are 0.
>
> >> >> I also want to try use longer time series to get the frequency fM,
> >> then
> >> >> for the shorter time series I can extract the frequency component
> for
> >> fM.
>
> >> >So what you *really* want to do is to decode an FM signal?
>
> >> >> The problem is there is no frequency from FFT exactly equal to fM.
> So
> >> how
> >> >> can I extract the component from the shorter time series based on
> fM
> >> >> calculated by longer time series. I know we can interpolate by
> >> >> zero-padding, But I feel I can not extract the exact component from
> >> this.
>
> >> >> Hope I made my problem clear. Thank you all
>
> >> >No, you haven't. What do you try to do? Estimate the frequency of
> >> >one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?
>
> >> >Rune
> >> >===============
>
> >> Thank you Rune,
> >> To clarify my problem, I want to estimate accurately the frequency of
> one
> >> sinusoidal, not separate two sinusoidals because there is only one
> main
> >> frequency in my signal. My problem is strongly depends on the
> frequency
> >> resolution, which means small frequency change will introduce big error
> in
> >> my problem. basically, I need the resolution about 0.01-0.02Hz.
>
> >You need 50-100 s of data to get that.
>
> >> The wave signal I recorded is about 40-50s. But because it is hard to
> >> separate the reflected wave and incident wave for my situation, I need
> use
> >> only the beginning part to analysis (7s to 10s). So my second question
> is
> >> trying get the frequency from the whole signal which give the
> resolution
> >> about 0.02Hz, then use this frequency(lets say fM) to analysis the
> >> beginning part. Since 7s to 10s signal may not give extact fM
> component,
> >> how can I extract the fM component from this short period.
>
> >What type of signal is this? You talk about 'pulse' and 'reflection'.
> >Those are usually transients, meaning that frequency estimation
> >is more or less meaningless since you transmitted the signal
> >yourself and - presumably - already know what you sent.
>
> >Could you please decribe the experiment and application?
>
> >Rune
> >===============================
>
> Rune, I measure the gravity water wave propagating into ice cover in the
> lab. The wave will reflect from the beach. Because the wave damps under ice
> cover, it is hard to separate the incident wave and reflected wave. For my
> analysis, I need use the pure incident wave which means there is no
> reflection, I call it the beginning part in my last post. I assume that the
> wave paddle only generate one frequency.

Why do you think that the frequency of th ereflection will change?
If it does not, then use the whole signal irrespective of reflections.
Ih it does (for instance because of propagations in shallow waters)
then use the whole signal. In the latter case the change in frequency
is likely to be so large that the waves are well-separated in frquency
domain.

Rune

>On 23 Jul, 00:24, "biantai" <wrxd...@gmail.com> wrote:
>> >On 22 Jul, 19:11, "biantai" <wrxd...@gmail.com> wrote:
>> >> >On 22 Jul, 02:50, "biantai" <wrxd...@gmail.com> wrote:
>> >> >> Hi all,I am a newer in DSP. I have a frequency resolution
problem,
>> >> need
>> >> >> your suggestions and comments.
>>
>> >> >> My problem depends on frequency resolution. Basically I need the
>> >> frequency
>> >> >> resolution around 0.01-0.02 at least to make the error smaller.
But
>> my
>> >> >> useful signal is roughly 10s which means the frequency
resolution
>> is
>> >> 0.1Hz,
>> >> >> this is far away from my requirement. Does anybody know if there
is
>> >> method
>> >> >> can solve this issue?
>>
>> >> >It depends on the exact problem you try to solve. "Resolution" can
>> >> >mean
>> >> >two things, either the ability to find the frequeny of *one*
>> >> >sinusoidal
>> >> >with high accuracy, or to separate *two* sinusoidals at similar
>> >> >frequencies.
>>
>> >> >The available solution methods depend on what you try to do and
why.
>>
>> >> >> One of my friends suggested me to patch the "good connected
signal"
>> >> from
>> >> >> the original signal to the end of the time series to make the
>> signal
>> >> very
>> >> >> long. I don't think this will work, but I don't know how to
argue
>> with
>> >> him.
>> >> >> Anybody can give me a theory for this so that I can argue with
him.
>>
>> >> >It's an interesting exercise if you try it, but it will not solve
>> >> >your
>> >> >problem since you do not introduce new information to the signal.
>>
>> >> >Try this in matlab:
>>
>> >> >s=randn(100,1);
>> >> >stem((0:length(s)-1)/length(s),abs(fft(s)),'b');
>> >> >hold on
>> >> >S=[s;s];
>> >> >stem((0:length(S)-1)/length(S),abs(fft(S))/2,'r')
>>
>> >> >It should be no surprise that you get all the same coefficients
>> >> >in the extended signal as in the original signal (save a scale
>> >> >factor). Since you did not add any new information, the 'extra'
>> >> >coefficients in the spectrum of the extended sequence are 0.
>>
>> >> >> I also want to try use longer time series to get the frequency
fM,
>> >> then
>> >> >> for the shorter time series I can extract the frequency
component
>> for
>> >> fM.
>>
>> >> >So what you *really* want to do is to decode an FM signal?
>>
>> >> >> The problem is there is no frequency from FFT exactly equal to
fM.
>> So
>> >> how
>> >> >> can I extract the component from the shorter time series based
on
>> fM
>> >> >> calculated by longer time series. I know we can interpolate by
>> >> >> zero-padding, But I feel I can not extract the exact component
from
>> >> this.
>>
>> >> >> Hope I made my problem clear. Thank you all
>>
>> >> >No, you haven't. What do you try to do? Estimate the frequency of
>> >> >one sinusoidal? Separate two sinusoidals? Demodulate an FM signal?
>>
>> >> >Rune
>> >> >===============
>>
>> >> Thank you Rune,
>> >> To clarify my problem, I want to estimate accurately the frequency
of
>> one
>> >> sinusoidal, not separate two sinusoidals because there is only one
>> main
>> >> frequency in my signal. My problem is strongly depends on the
>> frequency
>> >> resolution, which means small frequency change will introduce big
error
>> in
>> >> my problem. basically, I need the resolution about 0.01-0.02Hz.
>>
>> >You need 50-100 s of data to get that.
>>
>> >> The wave signal I recorded is about 40-50s. But because it is hard
to
>> >> separate the reflected wave and incident wave for my situation, I
need
>> use
>> >> only the beginning part to analysis (7s to 10s). So my second
question
>> is
>> >> trying get the frequency from the whole signal which give the
>> resolution
>> >> about 0.02Hz, then use this frequency(lets say fM) to analysis the
>> >> beginning part. Since 7s to 10s signal may not give extact fM
>> component,
>> >> how can I extract the fM component from this short period.
>>
>> >What type of signal is this? You talk about 'pulse' and 'reflection'.
>> >Those are usually transients, meaning that frequency estimation
>> >is more or less meaningless since you transmitted the signal
>> >yourself and - presumably - already know what you sent.
>>
>> >Could you please decribe the experiment and application?
>>
>> >Rune
>> >===============================
>>
>> Rune, I measure the gravity water wave propagating into ice cover in
the
>> lab. The wave will reflect from the beach. Because the wave damps under
ice
>> cover, it is hard to separate the incident wave and reflected wave. For
my
>> analysis, I need use the pure incident wave which means there is no
>> reflection, I call it the beginning part in my last post. I assume that
the
>> wave paddle only generate one frequency.
>
>Why do you think that the frequency of th ereflection will change?
>If it does not, then use the whole signal irrespective of reflections.
>Ih it does (for instance because of propagations in shallow waters)
>then use the whole signal. In the latter case the change in frequency
>is likely to be so large that the waves are well-separated in frquency
>domain.
>
>Rune
>=============
Rune, thank you for your reply. Maybe I am not clear to describe this
problem. I also think the frequency will not change, so I try to use the
whole signal to determine the frequency. But because I also need get ride
of the noise in my pure wave part which only means no reflection but noise,
I need to extract the frequency component from it. 
So the problem becomes to how to extract the main frequency component for
a short sequence when I know the main frequency?