vector-fftw-0.1.3: A binding to the fftw library for one-dimensional vectors.

Safe HaskellNone




This module provides normalized versions of the transforms in fftw.

All of the transforms are normalized so that

  • Each transform is unitary, i.e., preserves the inner product and the sum-of-squares norm of its input.
  • Each backwards transform is the inverse of the corresponding forwards transform.

(Both conditions only hold approximately, due to floating point precision.)

For more information on the underlying transforms, see


Creating and executing Plans

run :: (Vector v a, Vector v b, Storable a, Storable b) => Transform a b -> v a -> v bSource

Create and run a Plan for the given transform.

plan :: (Storable a, Storable b) => Transform a b -> Int -> Plan a bSource

Create a Plan of a specific size. This function is equivalent to planOfType Estimate.

execute :: (Vector v a, Vector v b, Storable a, Storable b) => Plan a b -> v a -> v bSource

Run a plan on the given Vector.

If planInputSize p /= length v, then calling execute p v will throw an exception.

Complex-to-complex transforms

dft :: Transform (Complex Double) (Complex Double)Source

A discrete Fourier transform. The output and input sizes are the same (n).

y_k = (1/sqrt n) sum_(j=0)^(n-1) x_j e^(-2pi i j k/n)

idft :: Transform (Complex Double) (Complex Double)Source

An inverse discrete Fourier transform. The output and input sizes are the same (n).

y_k = (1/sqrt n) sum_(j=0)^(n-1) x_j e^(2pi i j k/n)

Real-to-complex transforms

dftR2C :: Transform Double (Complex Double)Source

A forward discrete Fourier transform with real data. If the input size is n, the output size will be n `div` 2 + 1.

dftC2R :: Transform (Complex Double) DoubleSource

A normalized backward discrete Fourier transform which is the left inverse of dftR2C. (Specifically, run dftC2R . run dftR2C == id.)

This Transform behaves differently than the others:

  • Calling plan dftC2R n creates a Plan whose output size is n, and whose input size is n `div` 2 + 1.
  • If length v == n, then length (run dftC2R v) == 2*(n-1).

Discrete cosine transforms

Some normalized real-even (DCT). The input and output sizes are the same (n).

dct2 :: Transform Double DoubleSource

A type-2 discrete cosine transform. Its inverse is dct3.

y_k = w(k) sum_(j=0)^(n-1) x_j cos(pi(j+1/2)k/n); where w(0)=1/sqrt n, and w(k)=sqrt(2/n) for k>0.

idct2 :: Transform Double DoubleSource

A type-3 discrete cosine transform which is the inverse of dct2.

y_k = (-1)^k w(n-1) x_(n-1) + 2 sum_(j=0)^(n-2) w(j) x_j sin(pi(j+1)(k+1/2)/n); where w(0)=1/sqrt(n), and w(k)=1/sqrt(2n) for k>0.

dct4 :: Transform Double DoubleSource

A type-4 discrete cosine transform. It is its own inverse.

y_k = (1/sqrt n) sum_(j=0)^(n-1) x_j cos(pi(j+1/2)(k+1/2)/n)