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Within LTS Haskell 24.39 (ghc-9.10.3)
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idct4 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Invertible A type-4 discrete cosine transform which is the inverse of dct4.
y_k = (1/n) sum_(j=0)^(n-1) x_j cos(pi(j+1/2)(k+1/2)/n)
idft :: Transform (Complex Double) (Complex Double)vector-fftw Numeric.FFT.Vector.Invertible A backward discrete Fourier transform which is the inverse of dft. The output and input sizes are the same (n).
y_k = (1/n) sum_(j=0)^(n-1) x_j e^(2pi i j k/n)
idst1 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Invertible A type-1 discrete sine transform which is the inverse of dst1.
y_k = (1/(n+1)) sum_(j=0)^(n-1) x_j sin(pi(j+1)(k+1)/(n+1))
idst2 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Invertible A type-3 discrete sine transform which is the inverse of dst2.
y_k = (1/(2n)) [(-1)^k x_(n-1) + 2 sum_(j=0)^(n-2) x_j sin(pi(j+1)(k+1/2)/n)]
idst3 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Invertible A type-2 discrete sine transform which is the inverse of dst3.
y_k = (1/n) sum_(j=0)^(n-1) x_j sin(pi(j+1/2)(k+1)/n)
idst4 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Invertible A type-4 discrete sine transform which is the inverse of dst4.
y_k = (1/(2n)) sum_(j=0)^(n-1) x_j sin(pi(j+1/2)(k+1/2)/n)
idft :: TransformND (Complex Double) (Complex Double)vector-fftw Numeric.FFT.Vector.Invertible.Multi A backward discrete Fourier transform which is the inverse of dft. The output and input sizes are the same (n).
idct2 :: Transform Double Doublevector-fftw Numeric.FFT.Vector.Unitary 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.
idft :: Transform (Complex Double) (Complex Double)vector-fftw Numeric.FFT.Vector.Unitary 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)
idft :: TransformND (Complex Double) (Complex Double)vector-fftw Numeric.FFT.Vector.Unitary.Multi 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)