# FFT Matlab - What is a N-point FFT?

Started by April 15, 2006
```jpopovich@gmail.com skrev:
> Thank you for the response!
>
> What do you mean by "Y value"?
>
> For example:
>
> x=data(1:1024);
> 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

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)         [1]

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)     [2]

Note that there is no scaling factor in front of [1] and a factor
1/N in front of [2]. This is a matter of convention.

You would have observed the same amplitudes for all
FFT lengts if both the forward transform [1] and the inverse
transform [2] were scaled by 1/sqrt(N).

Rune

```
```Thank you very much.  This has been very helpful!

```