dffti

Purpose

Computes inverse discrete Fourier transform.

Format

y = dffti(x)
Parameters:x (Nx1 vector) – values used to computer the inverse of the discrete Fourier transform.
Returns:y (Nx1 vector) – the inverse discrete Fourier transform.

Examples

// Set k
k = seqa(0, 1, 4);

// Compute discrete frequencies
f_k = 5 + 2 * cos(pi/2*k - 90*pi/180) + 3 * cos(pi*k);

After this f_k is equal to:

8
4
8
0
// Discrete Fourier transform
x = dfft(f_k);

// Inverse Fourier transform
y = dffti(x);

Now:

x =   5
      0 -      1i
      3 +      0i
      0 +      1i

y =   8 +      0i
      4 +      0i
      8 +      0i
      0 +      0i

Remarks

The transform is divided by \(N\).

This uses a second-order Goertzel algorithm. It is considerably slower than ffti(), but it may have some advantages in some circumstances. For one thing, \(N\) does not have to be an even power of 2.

Source

dffti.src

See also

fft(), dffti(), ffti()