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Finding Frequency of signal with time and amplitude data using python

I have a data that has two columns time and corresponding amplitude of signal. I need to compute the frequency of the signal. How can do this. I read about scipy and numpy fft. But I really do not understand how to use them in my case.
Lift Coefficient vs Time
I need to Calculate the frequency for the signal that is after time say 4s. which seems periodic.

How to detect sine pattern in a signal or time-series data?

I need to detect sine patterns in time-series data. Data includes small oscillations and a few numbers of sine patterns. What I need is [Start Time, End Time] of sine pattern.
Please note that there is a timestamp (0.5 second) to get data. Therefore, data is not continuous.
I appreciate it if you introduce any algorithm.
Also, if the algorithm is already implemented in a python library, please guide me.

You may try FFT method to find a sine frequency, then use correlation with the model signal to bind it with time domain. Also you could use spectrogram analysis to get picture of your signal in time-frequency (it should looks like a line in time with the beginning and the end).
For example four sines with different frequencies may looks like on the spectrogram:

How to find the FFT of an unevenly sampled signal in python3?

I have a data with unevenly spaced (time) samples. How can I find the FFT of the signal and plot it.

Apart from the suggested answers, if your goal is find the frequencies (and not have to use FFT for some reason - which I can't infer from your question), you can consider using periodograms; more specifically, the Lomb-Scargle Periodogram - which can yield frequencies corresponding to unevenly spaced data.
Here is a great answer illustrating this suggestion.

You can't do an FFT of an unevenly sampled signal. That invalidates the assumptions of the math the FFT is based upon.
You'll have to resample the signal so you have evenly spaced samples.
This is slightly out of scope of this forum, but you can start in the dsp stackexchange
If you want a quick and dirty solution use the following approach :
choose a time delay less than or equal your smallest time between points --> dt or alternatively 20% of the inverse of the maximum frequency you are interested in.
make a buffer with N points with N a power of 2 and N*dt > Tmax - Tmin, or whatever the time window you are interested in.
distribute your points over the 2 closest points, or if you do not mind a bit more 'fuzz' just put it at the nearest point.
You'll end up with a buffer with spikes and zeroes in it, but with the same energy as your original signal.
Now FFT and only use the lowest 20% or so of the frequency lines.
This is an incredibly 'raw' and 'approximative' way of doing things, but it will give some approximation of wiggly power bars over frequency. You can clean the signal up by applying windows.
Note that digital signal processing is a field unto itself. I recommend to explore that rabbithole, but do expect to spent quite some time down there.

To use an FFT, you will need to created a vector of samples evenly spaced in time.
If the signal was bandlimited to below a sample rate implied by the widest sample spacings, you can try polynomial interpolation between your unevenly spaced samples to create a grid of about the same number of equally spaced samples in time. But, depending on polynomial degree, this might be highly sensitive to any noise in the bandlimiting or sampling process.

Using fourier analysis for time series prediction

For data that is known to have seasonal, or daily patterns I'd like to use fourier analysis be used to make predictions. After running fft on time series data, I obtain coefficients. How can I use these coefficients for prediction?
I believe FFT assumes all data it receives constitute one period, then, if I simply regenerate data using ifft, I am also regenerating the continuation of my function, so can I use these values for future values?
Simply put: I run fft for t=0,1,2,..10 then using ifft on coef, can I use regenerated time series for t=11,12,..20 ?

I'm aware that this question may be not actual for you anymore, but for others that are looking for answers I wrote a very simple example of fourier extrapolation in Python https://gist.github.com/tartakynov/83f3cd8f44208a1856ce
Before you run the script make sure that you have all dependencies installed (numpy, matplotlib). Feel free to experiment with it.
P.S. Locally Stationary Wavelet may be better than fourier extrapolation. LSW is commonly used in predicting time series. The main disadvantage of fourier extrapolation is that it just repeats your series with period N, where N - length of your time series.

It sounds like you want a combination of extrapolation and denoising.
You say you want to repeat the observed data over multiple periods. Well, then just repeat the observed data. No need for Fourier analysis.
But you also want to find "patterns". I assume that means finding the dominant frequency components in the observed data. Then yes, take the Fourier transform, preserve the largest coefficients, and eliminate the rest.
X = scipy.fft(x)
Y = scipy.zeros(len(X))
Y[important frequencies] = X[important frequencies]
As for periodic repetition: Let z = [x, x], i.e., two periods of the signal x. Then Z[2k] = X[k] for all k in {0, 1, ..., N-1}, and zeros otherwise.
Z = scipy.zeros(2*len(X))
Z[::2] = X

When you run an FFT on time series data, you transform it into the frequency domain. The coefficients multiply the terms in the series (sines and cosines or complex exponentials), each with a different frequency.
Extrapolation is always a dangerous thing, but you're welcome to try it. You're using past information to predict the future when you do this: "Predict tomorrow's weather by looking at today." Just be aware of the risks.
I'd recommend reading "Black Swan".

you can use the library that #tartakynov posted and, to not repeat exactly the same time series in the forcast (overfitting), you can add a new parameter to the function called n_param and fix a lower bound h for the amplitudes of the frequencies.
def fourierExtrapolation(x, n_predict,n_param):
usually you will find that, in a signal, there are some frequencies that have significantly higher amplitude than others, so, if you select this frequencies you will be able to isolate the periodic nature of the signal
you can add this two lines who are determinated by certain number n_param
h=np.sort(x_freqdom)[-n_param]
x_freqdom=[ x_freqdom[i] if np.absolute(x_freqdom[i])>=h else 0 for i in range(len(x_freqdom)) ]
just adding this you will be able to forecast nice and smooth
another useful article about FFt:
forecast FFt in R

Power spectral density of a signal with gaps?

Does anyone know if it is possible to find a power spectral density of a signal with gaps in it. For example (in matlab syntax cause that is what I'm familiar with)
ta=1:1000;
tb=1200:3000;
t=[ta tb]; % this is the timebase
signal=randn(size(t)); this is a signal
figure(101)
plot(t,signal,'.')
I'd like to be able to determine frequencies on a longer time base that just the individual sections of data. Obviously I could just take the PSD of individual sections but that will limit the lowest frequency. I could interpolate the data, but this would colour the PSD.
Any thoughts would be much appreciated.

The Lomb-Scargle periodogram algorithm is usually used to perform analysis on unevenly spaced data (sampled at arbitrary time points) or when a proportion of the data is missing.
Here's a couple of MATLAB implementations:
lombscargle.m (FEX)
Lomb (Lomb-Scargle) Periodogram (FEX)
lomb.m - ECG tools by Gari Clifford

I found this Non Uniform FFT but I'm not sure that its exactly what I need as it might really be for data that is mostly sampled on an uneven time base, rather than evenly spaced data with significant gaps. I'll give it a go!

Leaving out segments of the Fourier basis vectors results in exactly the same FT, thus PSD, as using the complete basis, but multiplying by zeros within a zero padding in any signal "gaps".