Fourier transform of sampled data

I have got some impulse response data that I would like to transform via Fourier to get the amplitude-frequency characteristics of the performing loudspeaker. The final goal is to show (e.g. via ListDensityPlot) how the calculated amplitude-frequency characteristics is dependant on the window I choose to transform (truncation of low frequencies). The issue I have is to get Fourier to behave like desired - I am unable to reproduce the frequency response that I got out of another 3rd part software. The issue:

There is no SampleRate option for Fourier (and I got a sampling frequency of 48kHz)

The following example illustrates the issues:

data = Table[Sin[x], {x, 0, 100}];

ListPlot[
Take[10*Log10[(Abs@Fourier[data, FourierParameters -> {1, -1}])^2], 
Floor@(Length[Fourier[data, FourierParameters -> {1, -1}]]/2)], 
Joined -> True, PlotRange -> Full]

fourier

Periodogram[data, FourierParameters -> {1, -1}, SampleRate -> 1, 
PlotRange -> Full, ScalingFunctions -> "dB"]

periodogram

Answer

samplerate = 48000;
time = Length[data]/samplerate;
nyq = Floor[Length[data]/2]; 
ListPlot[

 Take[10*Log10[(Abs@Fourier[data, FourierParameters -> {1, -1}])^2], nyq], 
 Joined -> True, PlotRange -> Full, 
 DataRange -> {0, (nyq - 1)/time}]

enter image description here

Compare with periodigram with given sample rate of 48 kHz:

Periodogram[data, FourierParameters -> {1, -1}, SampleRate -> 48000, 
 PlotRange -> Full, ScalingFunctions -> "dB"]

enter image description here

Comments

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