How to calculate appropriate DFT without typical sampling frequency?

Dear community,

I am not good in signal processing. I need to calculate a single sided power spectral density of a signal, which is called 'g' in my code, but i am not able to get it completely correct (Sampling frequency issues i gues).

%% Investigate window function

clear

close

clc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% Params %%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Tleng = 50; % simulated time length [ms]

dt = 0.01; % time step [ms]

% time vector

t = (0:round(Tleng/dt)-1)*dt; % time vector

spike = zeros(size(t));

spike(1) = 1; % Make amplitude

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%% Generate alpha function %%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tau = 3.2; Amp = 1; window_shape = {'alpha'};

g = Synapse (spike, dt, tau, Amp, window_shape);

subplot(2,1,1)

plot ( t , g )

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%% DFT (Internet example which is probalbly not correct) %%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fs=100000; %sampling frequency

NFFT = 1024;

X = fft(g,NFFT);

X = X(1:NFFT/2+1);%Throw the samples after NFFT/2 for single sided plot

Pxx=X.*conj(X)/(NFFT*NFFT);

f = fs*(0:NFFT/2)/NFFT; %Frequency Vector

subplot(2,1,2)

plot(f/1000,10*log10(Pxx),'r');

title('Single Sided - Power Spectral Density');

xlabel('Frequency (kHz)')

ylabel('Power Spectral Density- P_{xx} dB/Hz');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%% Function for Synapse %%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function g = Synapse (spikes, dt, tau, Asyn, window_shape)

% This synapse is build to stimulate the IF-Model.

% *** INPUT PARAMETERS ***

% spikes: : spike vector (to show the number of inputs at each step)

% dt : size of time step [ms]

% c : input amplitude [coulomb]

% tau : time constant [ms]

% Asyn : synaptic input amplitude

% window_shape : determination of window

%

% *** OUTPUT PARAMETERs ***

% g : simulated synaptic input waveform [nS]

% Select window shape

window_shape = cell2mat(window_shape);

switch window_shape

case 'alpha'

% creating output vector

g = zeros(1,length(spikes));

% initial values

x = 0;

y = 0;

% factors used for calculation

format long % Genrate more digits

eulers_number = exp(1); % Generate eulers number

format short % Reduce number of digits for better speed

tau = tau / eulers_number; % Standardise with factor. This factor is based on eulers number

aa = Asyn * exp(1.0) / tau; % amplitude factor for normalizing the input

ee = exp(-dt/tau); % decrease factor used at each time step

% step-by-step calculation

for t = 1:length(spikes)

y = ee*y + aa*spikes(t);

x = ee*x + dt*y;

g(t) = x; % store data

end

end

end

[Paul Hinze]

This is how it looks at the moment