I have a measured quantity, X which varies with time. I want to do frequency analysis and find out the maximum and minimum frequency and at what time they occurs. I'm using Fast Fourier Transform method in Matlab. I'm able to generate amplitude spectrum which varies with time, but the problem is my maximum frequency is occurring at 0Hz. I think, there is some noise in my data. Is there any other approach to remove the noise and figure out maximum and minimum frequency?
Perhaps your quantity X has strong "DC" bias (DC->0Hz), i.e. the mean value is not zero(ish)? 0 Hz is probably the minimum frequency?
With best regards
Paul
To properly resolve the minimum frequency, you may need to increase the number of samples that you are analysing
Hugh Lachlan Kennedy and Paul Annus Currently, I have around 20,000 data points(samples) with a sampling frequency of 10 Hz. I also tried to calculate the mean and tried to subtract it from my variable and in this case, the maximum amplitude occurs at somewhere 0.0002 Hz, otherwise the maximum amplitude occurs at 0 Hz.Please correct if i'm thinking wrong. The maximum frequency occurs at the maximum amplitude of the spectrum and similarly with the minimum frequency at the minimum amplitude. You can have a look at the single sided amplitude spectrum of my data in the image attached and this image is a zoomed version.
To reduce the variance of your spectral estimate, try using Bartlett's or Welch's method. Play around with different window sizes, types and overlap. Hopefully this will clean things up a bit and allow you to see things in the spectrum that are currently obscured.
Also, maybe there is not min/max frequency, just a weighted continuum.
Hugh Lachlan Kennedy Thanks for your reply. I tried Welch Estimate in Matlab. Now I'm getting better results compared to earlier single sided amplitude spectrum. I tried with windowing and overlapping, but I didn't find much difference with normal Welch estimate and with windowing. I also confused upper and lower frequency with maximum and minimum frequency. I'm interested in the bandwidth of the spectrum. and the time at which they occur. Given the spectrum, bandwidth and amplitude, is it possible to find the time at cut off frequency or at the frequency where magnitude is -3 dB
Please find attachment of Welch power spectral density
Introducing time-variation adds another level of complexity. You may need to reconsider what you are trying to acheive here.
Maybe it would be better to use prior knowledge of the signal you are interested in and use a band-pass filter to extract what you want. Don't worry about trying to do it adaptively.
You can use the DWT to analyze your signal to say 3 levels, use daubechies 4 filter, then apply a threshold on the “details” of every level, then reconstruct your signal which will be a denoised exact reconstructed signal.
From here, you can apply your fft algorithm to see the frequency components of your signal.
I also suggest that you firstly do a down conversion by say 10 to reduce the number of samples you have. This will not affect your frequency components at all.
Check the analysis of your data with a certain reference. Is it correct that it has very low frequency such in your data.
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