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Latest activity Answered En Una Cajita De Oro - Augustine Ramirez - Mi Nueva Epoca qj fan qj fan view profile. I successfully pick up most of the major tidal species, however I can't seem to be able to pick up the fortnightly component Mfeven though it is apparent in the time domain.
Please see the link to the image Alert - Spectral Tide (File). Does anyone have any suggestions as Alert - Spectral Tide (File) why this is? Alert - Spectral Tide (File) Young David Young view profile. Cancel Copy to Clipboard. Is it possible to attach the actual data, or a link to it?
Donald John Donald John view profile. Hi, thank you for your response. Attached is the raw data. The output from the FFT is also attached. Tags fft frequency tide frequency analysis. See Also. David Young view profile. Vote 3. Answer by David Young David Young view profile. Edited by David Young David Young view profile. Accepted Answer. The apparent fortnightly frequency is in fact a beat pattern - there is little energy at this frequency and the low-frequency noise masks any peak there in the FFT.
In fact, there is a component in the gravitational potential with a fortnightly frequency, but its amplitude is relatively small. In fact, your data do show good agreement with the expected peaks. The Alert - Spectral Tide (File) below demonstrates it - if you run it you will see that the red tick marks at the twice-daily frequencies line up very nicely with the peaks in your data.
Only the largest diurnal component is visible above the noise, but you also have strong thrice-daily and four-times-daily peaks. Note that it's useful to plot only the low-frequency end of the spectrum, and taking logs makes the lower peaks much easier to see. Also removing the mean helps visibility and accuracy. Incidentally, the FFT isn't a good way to estimate the amplitude and phase of tidal components, if that's what you aim to do.
It's much better Dedale - Various - La Brocante MP3 do a direct least-squares fit of waves at the known frequencies. The FFT is fundamentally a bad method for estimating tidal component amplitudes, because it fits sinusoids whose periods divide exactly into the time span of the series.
These periods won't coincide with the tidal periods, so errors are introduced. The simplest alternative is to Alert - Spectral Tide (File) a model made of sinusoids at the known tidal frequencies, and this works very well. The least-squares approach is known as "classical harmonic analysis", for example in this PowerPoint presentation by Russ Herman. It has the additional advantage that missing data are not a problem. A basic function that carries out harmonic analysis is attached.
You can check out the results by estimating the amplitudes, then seeing how a resynthesised time series, plotted below in red, compares with the original, plotted in blue:. There are visible mismatches. I suspect this is because my array of frequencies does not include the 3-cycles-per-day and higher frequencies which are prominent in the Newhaven data.
You can also compare in the frequency domain, by looking at the power spectrum of the residuals, like this:. Adding more frequencies would clearly improve the fit. However, harmonic analysis is still relatively unsophisticated, and there's a big literature in the Alert - Spectral Tide (File), going back to George Darwin.
One way to improve on the simple function attached is to get error estimates, and a good paper dealing with this is here. It may also be well worth checking out some of the other toolboxes around, such as this one on the FEX. Finally, I think it's worth having a look at the nineteenth-century version of my attached file harmonicSynth. Thank you for this very comprehensive reply, it is incredibly useful.
Would you be able to point me in the direction of an explanation as to the beat pattern effect, I was under the impression that the fortnightly frequency is in fact a significant energy component of the tide. Finally do you have any pointers for the least square method you outline? I don't have an obvious reference, but textbooks on acoustics, signal processing and the Fourier transform should be helpful.
The Wikipedia article on beats Alert - Spectral Tide (File) quite helpful. The first equation shows how beats arise from the sum of two sine waves of close frequencies. Since the FT picks apart signals into a sum of sine waves, it will analyse the signal into those two original frequencies f1 and f2 in the Wikipedia articlenot into the beat frequency.
I'll try and get back shortly on fitting sinusoids to time series. A correction to my answer. You're right that there is a real peak with a fortnightly period in the spectrum of the gravitational potential; as you say, it's Mf. I had forgotten about it. However, you don't see it in your data because it's lost in the low-frequency noise. The effect that you see in the graph of the time series - the change in the envelope between spring and neap tides - is beating between nearby semidiurnal and diurnal frequencies, mainly between S2 and M2, and is not due to the Mf component.
Okay, I think that makes sense. Is there other methods that could be applied to pick up the Mf component? For example would the least squares method you mentioned prove useful here? I think the Mf component is below the level of the low-frequency noise, and you are not likely to get a reliable estimate of its amplitude unless you can get hold of a much longer time series.
I'm about to edit the answer to include information about tidal component estimation. Thanks for the incredibly useful edit and extension to your answer. I am now trying to use the Lomb Scargle method, which is a least squares method. It is very useful because I have other data that is unevenly sampled. However I am having Alert - Spectral Tide (File) issue with a different data set, that has a much shorter time-series.
Is there anyway to improve the accuracy of peak estimates using short-time series with these least squares based methods? To improve the accuracy you need to introduce some constraints on the model - Alert - Spectral Tide (File) classical way is to assume that the response varies smoothly with frequency so that for nearby frequencies the amplitudes are in proportion to Кисель / Шепот (Dessert Made Of Fruit / Whisper) - Volga - Dom_Live amplitudes of the driving potential.
This seminal paper for this is Munk and Cartwright ; there may be more recent work that is less complex. Adi Purwandana Adi Purwandana view profile. Many thanks, Adi. Youssef Khmou view profile. Vote 0. Answer by Youssef Khmou Youssef Khmou view profile. Edited by Youssef Khmou Youssef Khmou view profile. From the result in the second figure; you can remark that there are two frequency components.
Thanks, I Grave Digger - Healed By Metal. These components are the However there is clearly a fortnightly frequency within the data from the top figure, the FFT analysis does not seem to pick this up.
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