Discrete Fourier transform: Difference between revisions
Added Go
m (→{{header|Perl}}: clarification on abbreviations) |
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The inverse transform is given by:
<math>x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k\cdot e^{i \frac{2 \pi}{N} k n}</math>
=={{header|Go}}==
{{trans|Wren}}
<lang go>package main
import (
"fmt"
"math"
"math/cmplx"
)
func dft(x []complex128) []complex128 {
N := len(x)
y := make([]complex128, N)
for k := 0; k < N; k++ {
for n := 0; n < N; n++ {
t := -1i * 2 * complex(math.Pi*float64(k)*float64(n)/float64(N), 0)
y[k] += x[n] * cmplx.Exp(t)
}
}
return y
}
func idft(y []complex128) []float64 {
N := len(y)
x := make([]complex128, N)
for n := 0; n < N; n++ {
for k := 0; k < N; k++ {
t := 1i * 2 * complex(math.Pi*float64(k)*float64(n)/float64(N), 0)
x[n] += y[k] * cmplx.Exp(t)
}
x[n] /= complex(float64(N), 0)
// clean x[n] to remove very small imaginary values
if math.Abs(imag(x[n])) < 1e-14 {
x[n] = complex(real(x[n]), 0)
}
}
z := make([]float64, N)
for i, c := range x {
z[i] = float64(real(c))
}
return z
}
func main() {
z := []float64{2, 3, 5, 7, 11}
x := make([]complex128, len(z))
fmt.Println("Original sequence:", z)
for i, n := range z {
x[i] = complex(n, 0)
}
y := dft(x)
fmt.Println("\nAfter applying the Discrete Fourier Transform:")
fmt.Printf("%0.14g", y)
fmt.Println("\n\nAfter applying the Inverse Discrete Fourier Transform to the above transform:")
z = idft(y)
fmt.Printf("%0.14g", z)
fmt.Println()
}</lang>
{{out}}
<pre>
Original sequence: [2 3 5 7 11]
After applying the Discrete Fourier Transform:
[(28+0i) (-3.3819660112501+8.7840226349462i) (-5.6180339887499+2.8001689857495i) (-5.6180339887499-2.8001689857495i) (-3.3819660112501-8.7840226349462i)]
After applying the Inverse Discrete Fourier Transform to the above transform:
[2 3 5 7 11]
</pre>
=={{header|J}}==
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