Hello to all The problem is as follows: Intermittently, a signal is received whose duration can be in the range 2 to 100 msec, which is a FM wave, its frequency can vary from 15kHz to 100kHz. We are required to estimate the following characteristics of the signal 1. Frequency (accuracy within 10Hz) 2. signal slope within 3% The SNR is 30dB. I have used a sampling frequency of fs=250kHz. I am using zero crosing method of instantaneous frequency estimation, the accuracy seems to be OK, but it not that staight forward to fix the window size.(Window size, refers to the number of samples used to estimate the instantaneous frequency). Is there any rule of thumb, way to choose window size depending on fs, and the input signal range. How can I estimate the signal slope? Before we do all these processing, we have to detect the desired signal in the first place. We feel energy and frequency (not yet tested)is an adequate. criteria. Suggest any other suitale/possible criteria for this detection. All these, we hope to do it in real time. Please help Thanks in advance KK
Help with signal analysis
Started by ●March 25, 2004
Reply by ●March 25, 20042004-03-25
"KK" <surespam@rediffmail.com> wrote in message news:6d8d5524.0403250305.74e4a11b@posting.google.com...> Hello to all > > The problem is as follows: > Intermittently, a signal is received whose duration can be in the > range 2 to 100 msec, which is a FM wave, its frequency can vary from > 15kHz to 100kHz. > > We are required to estimate the following characteristics of the > signal > 1. Frequency (accuracy within 10Hz) > 2. signal slope within 3% > > The SNR is 30dB. > > I have used a sampling frequency of fs=250kHz. > > I am using zero crosing method of instantaneous frequency estimation, > the accuracy seems to be OK, but it not that staight forward to fix > the window size.(Window size, refers to the number of samples used to > estimate the instantaneous frequency). Is there any rule of thumb, way > to choose window size depending on fs, and the input signal range. > > How can I estimate the signal slope? > Before we do all these processing, we have to detect the desired > signal in the first place. We feel energy and frequency (not yet > tested)is an adequate. > criteria. Suggest any other suitale/possible criteria for this > detection. > > All these, we hope to do it in real time.KK, Well, first you should estimate the signal bandwidth. You say that it's FM but didn't say anything about the limit on the rate of change of frequency, etc. Unless it's NBFM, the bandwidth will be much greater than the frequency deviation. That means the sampling rate you've chosen could be much too low. Without the numbers, how is one to know? Another way to look at it: There's no way to get good zero-crossing information for a signal at 100kHz if the sample rate is only 250kHz. Or, do you mean that it's a frequency sweep as might be used in radar? By "slope", I take it you mean the rate of change of frequency. If the sample rate is very high then you have a chance of estimating frequency and rate of change of frequency - because you need to determine "instantaneous" frequency very accurately in a short period of time. Can you see that the objective of measuring frequency and the objective of measuring f rate of change are somewhat in conflict? A better measurement of frequency will involve averaging (integration) and measuring the rate of change will involve differentiation (differencing). So, the trick is in balancing the averaging time (short) against the responsiveness of the differentiator that follows. That's probably equivalent to the window you mention. With 30dB SNR you should be able to use simple energy detection. Another approach would be: just do the processing all the time and detect consistency in the output - a lack of variance in the frequency measure. Fred
Reply by ●March 31, 20042004-03-31
Hello
Fred,Thanks for your views.
I am becoming a bit pessimistic, about the accuracy in frequency
estimation needed. ...
Forget abou FM, sampling frequency for a while.
Given a signal(non-stationary) whose frequency changes in the
range 10kHz-100kHz. Can we estimate the instataneous frequency of this
signal within accuracy of 10Hz (i.e estimated freq - actual feq
<=10Hz)? Which methods can achieve this? Assuming that we can afford a
very high sampling frequency if needed.
Has any one solved some similar probelm with similar accuracy?
Thanks in advance
KK
Reply by ●March 31, 20042004-03-31
surespam@rediffmail.com (KK) writes:> I am becoming a bit pessimistic, about the accuracy in frequency > estimation needed. ... > Forget abou FM, sampling frequency for a while. > Given a signal(non-stationary) whose frequency changes in the > range 10kHz-100kHz. Can we estimate the instataneous frequency of this > signal within accuracy of 10Hz (i.e estimated freq - actual feq > <=10Hz)? Which methods can achieve this? Assuming that we can afford a > very high sampling frequency if needed. > Has any one solved some similar probelm with similar accuracy?What's the signal to noise ratio? Do you have any example data? Ciao, Peter K. -- Peter J. Kootsookos "I will ignore all ideas for new works [..], the invention of which has reached its limits and for whose improvement I see no further hope." - Julius Frontinus, c. AD 84
Reply by ●March 31, 20042004-03-31
Peter,> What's the signal to noise ratio?The SNR=30dB.> Do you have any example data?The signal is actually unknown, except for its frequency range. Presumably, the signal is something like x(t) = cos(2pi*f1*t) 0<t<=T1 cos(2pi*f2*t) T1<t<=T2 cos(2pi*f3*t) T2<t<=T3 ....... As I have written earlier, the frequencies are in the range 10kHz - 100kHz. Required frequency estimation accuracy of<=10Hz. KK
Reply by ●March 31, 20042004-03-31
"KK" <surespam@rediffmail.com> wrote in message news:6d8d5524.0403302335.296b37c8@posting.google.com...> Hello > Fred,Thanks for your views. > > I am becoming a bit pessimistic, about the accuracy in frequency > estimation needed. ... > Forget abou FM, sampling frequency for a while. > Given a signal(non-stationary) whose frequency changes in the > range 10kHz-100kHz. Can we estimate the instataneous frequency of this > signal within accuracy of 10Hz (i.e estimated freq - actual feq > <=10Hz)? Which methods can achieve this? Assuming that we can afford a > very high sampling frequency if needed. > Has any one solved some similar probelm with similar accuracy?KK, I tried to address this earlier. Here is another outline: IF the signal to noise ratio is very high IF you can take long samples of the signal - length "X" IF the frequency changes only slightly compared to the desired resolution of frequency estimation in signal length "X". THEN you can estimate the frequency - more or less with a resolution of 1/X. Does this make sense to you? These are fundamental physical constraints. So, if you need 10Hz resolution, you need to sample a stationary (or nearly stationary) signal for 0.1 seconds with a high signal to noise ratio. This implies that the signal frequency does not change more than something like 5 Hz in 0.1 seconds / does not have a frequency rate of change greater than 50Hz/second. All of that is what I call "physics" in signal processing. There are no techniques involved here, just physical realities. You should take it from there to decide if your objectives are allowed by physics. Only then is it worthwhile to pursue "methods". Some methods may require even more stringent requirements. Fred
Reply by ●March 31, 20042004-03-31
Fred Marshall wrote: (snip)> I tried to address this earlier. Here is another outline:> IF the signal to noise ratio is very high > IF you can take long samples of the signal - length "X" > IF the frequency changes only slightly compared to the desired resolution of > frequency estimation in signal length "X". > THEN you can estimate the frequency - more or less with a resolution of 1/X.> Does this make sense to you? These are fundamental physical constraints.For the original question of instantaneous frequency measurement, yes.> So, if you need 10Hz resolution, you need to sample a stationary (or nearly > stationary) signal for 0.1 seconds with a high signal to noise ratio. This > implies that the signal frequency does not change more than something like 5 > Hz in 0.1 seconds / does not have a frequency rate of change greater than > 50Hz/second.> All of that is what I call "physics" in signal processing. There are no > techniques involved here, just physical realities.> You should take it from there to decide if your objectives are allowed by > physics. Only then is it worthwhile to pursue "methods".There are some other things that physics will allow in more general cases. If you have a low signal/noise periodic signal you can do signal averaging. If you have N samples of the signal your S/N improves by sqrt(N). That can be used to find the shape of a noisy signal with enough samples. Also, if you have a noisy periodic signal, the longer you sample it the more accurate you can determine the average frequency. One example of this is phase-locked loops which average out the noise in the signal. The S/N ratio and the number of samples available will determine how accurately the shape or frequency can be measured. -- glen
Reply by ●March 31, 20042004-03-31
surespam@rediffmail.com (KK) writes:> Hello to all > > The problem is as follows: > Intermittently, a signal is received whose duration can be in the > range 2 to 100 msec, which is a FM wave, its frequency can vary from > 15kHz to 100kHz. > > We are required to estimate the following characteristics of the > signal > 1. Frequency (accuracy within 10Hz) > 2. signal slope within 3% > > The SNR is 30dB. > > I have used a sampling frequency of fs=250kHz. > > I am using zero crosing method of instantaneous frequency estimation, > the accuracy seems to be OK, but it not that staight forward to fix > the window size.(Window size, refers to the number of samples used to > estimate the instantaneous frequency). Is there any rule of thumb, way > to choose window size depending on fs, and the input signal range. > > How can I estimate the signal slope? > Before we do all these processing, we have to detect the desired > signal in the first place. We feel energy and frequency (not yet > tested)is an adequate. > criteria. Suggest any other suitale/possible criteria for this > detection.Hi, Here's a completely different way to do it: convert the signal into an analytic version (if you don't know how, ask). A pure tone will then be in the complex form x[n] = e^(j*2*pi*f*n*T). You can compute the frequency then in two samples by f[n] = (phi[n] - phi[n-1])/T, where x[n] = r[n] * e^(j*"phi[n]). If these f[n] samples are noisy, then you can take several and average. You can get really fancy and ask Peter for some much more complex frequency analysis techniques, but this may do it. -- % Randy Yates % "Though you ride on the wheels of tomorrow, %% Fuquay-Varina, NC % you still wander the fields of your %%% 919-577-9882 % sorrow." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr
Reply by ●March 31, 20042004-03-31
surespam@rediffmail.com (Parthasarathy) writes:> Peter, > > > What's the signal to noise ratio? > > The SNR=30dB. > > > Do you have any example data? > > The signal is actually unknown, except for its frequency range. > Presumably, the signal is something like > x(t) = cos(2pi*f1*t) 0<t<=T1 > cos(2pi*f2*t) T1<t<=T2 > cos(2pi*f3*t) T2<t<=T3 ....... > As I have written earlier, the frequencies are in the range 10kHz - 100kHz. > Required frequency estimation accuracy of<=10Hz.Will try to post an example later today... apologies for not reading your original post... it didn't make it to my news server. Ciao, Peter K. -- Peter J. Kootsookos "I will ignore all ideas for new works [..], the invention of which has reached its limits and for whose improvement I see no further hope." - Julius Frontinus, c. AD 84
Reply by ●April 1, 20042004-04-01
Randy Yates <yates@ieee.org> writes:> You can get really fancy and ask Peter for some much more complex > frequency analysis techniques, but this may do it.Could be! I'll get playing... Ciao, Peter K. -- Peter J. Kootsookos "I will ignore all ideas for new works [..], the invention of which has reached its limits and for whose improvement I see no further hope." - Julius Frontinus, c. AD 84
