Returns the FFT of a voltage signal (in volts) with the amplitude response units dBV.

fftdBV.m

function [Xmag, Xarg] = fftdBV(x)
%FFTDBV Returns the FFT of a voltage signal (in volts) with the amplitude response units dBV.

% Number of samples
N = length(x);

% Scaling factor is sqrt(2) except for at DC when it is 1.
k  = [1, ones(1,N-1)*sqrt(2)];

% Calculate the scaled DFT.
X = fft(x)./N;

% Amplitude response must be scaled by RMS to peak ratio.
Xmag  = 20*log10(k.*abs(X));

% Find the unwrapped phase of the fft.
Xarg  = unwrap(angle(X));

end