Signal Processing Toolbox |

Discrete Fourier transform matrix

**Syntax**

**Description**

A *discrete Fourier transform matrix* is a complex matrix of values around the unit circle, whose matrix product with a vector computes the discrete Fourier transform of the vector.

returns the `A`

= ```
dftmtx(n)
```

`n`

-by-`n`

complex matrix `A`

that, when multiplied into a length `n`

column vector `x`

.

computes the discrete Fourier transform of `x`

.

The inverse discrete Fourier transform matrix is

**Examples**

In practice, the discrete Fourier transform is computed more efficiently and uses less memory with an FFT algorithm

than by using the Fourier transform matrix.

**Algorithm**

`dftmtx`

takes the FFT of the identity matrix to generate the transform matrix.

**See Also**

dfilt.statespace | digitrevorder |