Discrete Fourier transform: Difference between revisions

=={{header|Nim}}==

{{trans|Wren}}

<lang Nim>import complex, math, sequtils, strutils

func dft(x: openArray[Complex64]): seq[Complex64] =

let N = x.len

result.setLen(N)

for k in 0..<N:

for n in 0..<N:

let t = complex64(0, -2 * PI * float(k) * float(n) / float(N))

result[k] += x[n] * exp(t)

func idft(y: openArray[Complex64]): seq[Complex64] =

let N = y.len

result.setLen(N)

let d = complex64(float(N))

for n in 0..<N:

for k in 0..<N:

let t = complex64(0, 2 * PI * float(k) * float(n) / float(N))

result[n] += y[k] * exp(t)

result[n] /= d

# Clean result[n] to remove very small imaginary values.

if abs(result[n].im) < 1e-14: result[n].im = 0.0

func `$`(c: Complex64): string =

result = c.re.formatFloat(ffDecimal, precision = 2)

if c.im != 0:

result.add if c.im > 0: "+" else: ""

result.add c.im.formatFloat(ffDecimal, precision = 2) & 'i'

when isMainModule:

let x = [float 2, 3, 5, 7, 11].mapIt(complex64(it))

echo "Original sequence: ", x.join(", ")

let y = dft(x)

echo "Discrete Fourier transform: ", y.join(", ")

echo "Inverse Discrete Fourier Transform: ", idft(y).join(", ")</lang>

{{out}}

<pre>Original sequence: 2.00, 3.00, 5.00, 7.00, 11.00

Discrete Fourier transform: 28.00, -3.38+8.78i, -5.62+2.80i, -5.62-2.80i, -3.38-8.78i

Inverse Discrete Fourier Transform: 2.00, 3.00, 5.00, 7.00, 11.00</pre>