# 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. 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.

dffti.src