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I have measured this signal over time (where x is time in seconds and y is AC in D):

j = {{0., 0.46154}, {0.02, 0.96675}, {0.04, 1.30241}, {0.06, 1.12558}, {0.08, 1.04516}, {0.1, 1.07797}, {0.12, 1.0831}, {0.14, 0.95638}, {0.16, 1.32981}, {0.18, 1.14929}, {0.2, 1.24911}, {0.22, 0.97462}, {0.24, 1.07281}, {0.26, 1.24135}, {0.28, 1.40147}, {0.3, 1.04097}, {0.32, 1.10173}, {0.34, 0.83951}, {0.36, 1.03412}, {0.38, 0.80009}, {0.4, 0.76809}, {0.42, 0.56192}, {0.44, 0.71579}, {0.46, 0.68322}, {0.48, 0.51772}, {0.5, 0.47568}, {0.52, 0.58318}, {0.54, 0.44943}, {0.56, 0.33383}, {0.58, 0.22818}, {0.6, 0.22581}, {0.62, 0.18426}, {0.64, 0.27745}, {0.66, 0.19635}, {0.68, 0.05239}, {0.7, 0.148}, {0.72, 0.22115}, {0.74, 0.01575}, {0.76, 0.2249}, {0.78, 0.15707}, {0.8, 0.24286}, {0.82, 0.0513}, {0.84, 0.12376}, {0.86, 0.12438}, {0.88, 0.16583}, {0.9, 0.18076}, {0.92, 0.1926}, {0.94, 0.32903}, {0.96, -0.11003}, {0.98, 0.12049}, {1., 0.21877}, {1.02, 0.11694}, {1.04, 0.41252}, {1.06, 0.13882}, {1.08, -0.14369}, {1.1, 0.11915}, {1.12, 0.44889}, {1.14, 0.22621}, {1.16, 0.52716}, {1.18, 0.20754}, {1.2, -0.11932}, {1.22, 0.34455}, {1.24, 0.41418}, {1.26, 0.21961}, {1.28, 0.46736}, {1.3, 0.11459}, {1.32, -0.00613}, {1.34, 0.0469}, {1.36, 0.10676}, {1.38, 0.11179}, {1.4, 0.34027}, {1.42, 0.0819}, {1.44, 0.29088}, {1.46, -0.01968}, {1.48, 0.29715}, {1.5, 0.12735}, {1.52, 0.08953}, {1.54, 0.07267}, {1.56, 0.54783}, {1.58, 0.49115}, {1.6, 0.31281}, {1.62, 0.04104}, {1.64, 0.55937}, {1.66, 0.21637}, {1.68, 0.00265}, {1.7, 0.16154}, {1.72, 0.08477}, {1.74, 0.21248}, {1.76, 0.09853}, {1.78, 0.25793}, {1.8, 0.05154}, {1.82, 0.22015}, {1.84, 0.24385}, {1.86, 0.22789}, {1.88, 0.19323}, {1.9, 0.42341}, {1.92, 0.07702}, {1.94, 0.35671}, {1.96, 0.16094}, {1.98, 0.49207}, {2., 0.17836}, {2.02, 0.42719}, {2.04, 0.28668}, {2.06, 0.2785}, {2.08, 0.1528}, {2.1, 0.18308}, {2.12, 0.17727}, {2.14, 0.51663}, {2.16, 0.12559}, {2.18, 0.51182}, {2.2, 0.17213}, {2.22, 0.4294}, {2.24, 0.19069}, {2.26, -0.03253}, {2.28, 0.2581}, {2.3, 0.09465}, {2.32, 0.18766}, {2.34, 0.22913}, {2.36, 0.08958}, {2.38, 0.27689}, {2.4, 0.07678}, {2.42, 0.52352}, {2.44, 0.00826}, {2.46, 0.38851}, {2.48, 0.1192}, {2.5, 0.42282}, {2.52, 0.22188}, {2.54, 0.26671}, {2.56, 0.21127}, {2.58, 0.24593}, {2.6, 0.27011}, {2.62, 0.2517}, {2.64, 0.11801}, {2.66, 0.31566}, {2.68, -0.02324}, {2.7, 0.15799}, {2.72, 0.23538}, {2.74, 0.12538}, {2.76, 0.29127}, {2.78, 0.17229}, {2.8, 0.20953}, {2.82, 0.13453}, {2.84, 0.18642}, {2.86, 0.24405}, {2.88, 0.19806}, {2.9, 0.15746}, {2.92, 0.24181}, {2.94, 0.13605}, {2.96, 0.19012}, {2.98, 0.255}, {3., 0.2002}, {3.02, 0.14607}, {3.04, 0.0805}, {3.06, 0.33034}, {3.08, 0.1248}, {3.1, 0.30092}, {3.12, 0.18443}, {3.14, 0.10899}, {3.16, 0.24753}, {3.18, 0.28695}, {3.2, 0.13825}, {3.22, 0.21763}, {3.24, 0.29405}, {3.26, 0.10328}, {3.28, 0.274}, {3.3, 0.17086}, {3.32, 0.0552}, {3.34, 0.09843}, {3.36, 0.01479}, {3.38, 0.15408}, {3.4, 0.1202}, {3.42, 0.04191}, {3.44, 0.0487}, {3.46, 0.17443}, {3.48, 0.16489}, {3.5, 0.15475}, {3.52, 0.07557}, {3.54, 0.22331}, {3.56, 0.16151}, {3.58, 0.25486}, {3.6, 0.28833}, {3.62, 0.39515}, {3.64, 0.06053}, {3.66, 0.19549}, {3.68, 0.32904}, {3.7, 0.25243}}

I want to get the power spectrum, where the x axis is "Power (D*10^-2)" and y is "Frequency (Hz)".

I wanted to get something like this with grey and black lines: enter image description here

And then I want to get the mean power (D^2/Hz) for low (LFC) (0.1-0.60 Hz), medium (MFC) (0.61-0.99 Hz), and high (HFC) (1.0-2.3 Hz) frequency components of the signal.

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    $\begingroup$ "Periodogram" gives you the power spectrum. And "Spectrogram" gives you a time-frequency plot. $\endgroup$ Commented Feb 17 at 18:12
  • $\begingroup$ Hi Daniel, Thank you for your answer. I tried with periodogram but I get negative values for yy. $\endgroup$ Commented Feb 17 at 21:11
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    $\begingroup$ Yes, these are Decibels. If you want a linear scale you need to specify the option "ScalingFunctions". $\endgroup$ Commented Feb 17 at 21:24

1 Answer 1

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Clear["Global`*"]; samplingRate = 50; (*Samples per unit time,e.g.,Hz if time is in seconds*) duration = 1; (*Total duration of the signal*) numSamples = samplingRate*duration; frequencyRange = {0, samplingRate/2}; (*Create a time series with some frequencies*) timeSeries = Table[{t, 0.5*Sin[2 Pi 5 t] + 0.3*Cos[2 Pi 10 t] + 0.1*RandomReal[{-1, 1}]}, {t, 0, duration, 1/samplingRate}]; (*1. Power Spectrum (Periodogram)*) powerSpectrum = Periodogram[timeSeries[[All, 2]], SampleRate -> samplingRate, ScalingFunctions -> "PSD"]; (*Power Spectral Density*) (*Display the power spectrum*) Show[powerSpectrum, PlotRange -> All, AxesLabel -> {"Frequency", "Power Spectral Density"}, PlotLabel -> "Power Spectrum (Periodogram)", PlotRange -> Full]

You can replace timeSeries with your data, then it looks like:

enter image description here

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