> Thank you for the response!
> What do you mean by "Y value"?
> For example:
> y = fft(x, 1024);
> y2 = fft(x, 2056);
> y_mag = y.*conj(y) / 1024;
> y2_mag = y2.*conj(y2) / 2056;
> What I observed is that when each are plotted seperately, the shape is
> similar but the Y-axis values difffer.
> That is, the y2_mag value (2056-point fft) is smaller than the values
> for the y_mag (1024-point fft).
> Is this correct or am I doing something wrong? Thank you so much for
> your help!
There is a scaling constant in the DFT that causes the different
scales you observe.
The forward DFT of a sequence x(n) of length N is defined as
X(k) = sum_(n=0)^(N-1) x(n) exp(-j 2*pi*n*k/N) 
and the Inverse DFT is defined as
x(n) = 1/N sum_(k=0)^(N-1) X(k) exp(j 2*pi*n*k/N) 
Note that there is no scaling factor in front of  and a factor
1/N in front of . This is a matter of convention.
You would have observed the same amplitudes for all
FFT lengts if both the forward transform  and the inverse
transform  were scaled by 1/sqrt(N).