So I've run into some trouble in trying to plot the PSD of an OFDM signal. Specifically, I cant see how we go from the discrete domain to the continuous in time domain.

I have a time vector, which is sample at a rate of 10Khz, over a duration of 100s

t = 0:1/1e4:100

I then generate a signal by low-pass filtering some noise at a maximum frequency

f_max = 50;                                              % maximum freq of message signal
x     = randn(size(t));                                  % Generate some noise
x     = filter2(fir1(10*ceil(f_s/f_max),2*f_max/f_s),x); % Low pass filter the noise
x     = x-mean(x);                                       % Remove any DC offset
x     = x/sqrt(mean(x.^2));                              % Normalise the signal

This is my 'continuous in time' signal which is then sampled at a rate of 8Hz to give by discrete in time signal

f_sample          = 8;
number_of_symbols = f_sample*t(end);
sample_indices    = round((0:number_of_symbols -1)*(length(x)-1)/(number_of_symbols -1))+1;
xSampled          = x(sample_indices);

This is then quantised and QAM modulated in the discrete domain

xQuant = quantiz(xSampled,partition,codebook); % quantisation
xMod   = qammod(xQuant,M);                     % QAM modulation

This is where my problem comes. The next step for OFDM would then be to convert this frequency domain representation to a continuous in time representation using an IFFT. But lets say I have FFT_Length= 64, I'd split my QAM modulated signal into 64 vectors of length number_of_symbols/64, and this would give me 64 vectors out, each of length number_of_symbols/64, one for each subcarrier - we have remained in the discrete domain?

If this was a single carrier scheme this is when id apply pulse shaping to the QAM symbols and upsample the signal frequency to the original 10khz, however pulse shaping is not used in OFDM. I was thinking we could either upsample the QAM symbols prior to the OFDM modulation by padding with 0's for the remaineder of the symbol period, or do the same but pad with the QAM value, however in both cases the resulting FFT is like a square wave - stuck at a one value for a symbol period, then switches immediately to another.

So my question:

how do I convert a series of QAM pulses to a continuous time signal using the IFFT (in OFDM)

Many thanks :-)