---
title: Out-of-Place Functions for 1D Multiple-Signal Real FFT
framework: accelerate
role: collectionGroup
role_heading: API Collection
path: accelerate/out-of-place-functions-for-1d-multiple-signal-real-fft
---

# Out-of-Place Functions for 1D Multiple-Signal Real FFT

Perform fast Fourier transforms out of place on multiple-signal 1D real data.

## Overview

Overview The functions in this group use the following operation for a forward real-to-complex transform: N = 1 << Log2N;

// Repeat M times: for (m = 0; m < M; ++m) {      scale = 2;

// Define a real vector, h:      for (j = 0; j < N/2; ++j)      {          h[2*j + 0] = A->realp[m*IMA + j*IA];          h[2*j + 1] = A->imagp[m*IMA + j*IA];      }

// Perform Discrete Fourier Transform.      for (k = 0; k < N; ++k)          H[k] = scale *              sum(h[j] * e**(-Direction*2*pi*i*j*k/N), 0 <= j < N);

// Pack DC and Nyquist components into initial elements.      C->realp[m*IMC + 0*IC] = Re(H[ 0 ]).      C->imagp[m*IMC + 0*IC] = Re(H[N/2]).

// Store regular components:      for (k = 1; k < N/2; ++k)      {          C->realp[m*IMC + k*IC] = Re(H[k]);          C->imagp[m*IMC + k*IC] = Im(H[k]);      } }

The functions in this group use the following operation for an inverse complex-to-real transform: N = 1 << Log2N;

scale = 1./N;

// Repeat M times: for (m = 0; m < M; ++m) {

// Define a complex vector, h:     h[ 0 ] = A->realp[m*IMA + 0*IA];     h[N/2] = A->imagp[m*IMA + 0*IA];     for (j = 1; j < N/2; ++j)     {         h[ j ] = A->realp[m*IMA + j*IA]            + i * A->imagp[m*IMA + j*IA];         h[N-j] = conj(h[j]);     }

// Perform Discrete Fourier Transform.     for (k = 0; k < N; ++k)         H[k] = scale *             sum(h[j] * e**(-Direction*2*pi*i*j*k/N), 0 <= j < N);

// Coerce real results into complex structure:     for (k = 0; k < N/2; ++k)     {         C->realp[m*IMC + k*IC] = H[2*k+0];         C->imagp[m*IMC + k*IC] = H[2*k+1];     } }

The temporary buffer versions perform the same operation but use a temporary buffer for improved performance.

## See Also

### Functions for 1D Multiple-Signal Real FFT

- [In-Place Functions for 1D Multiple-Signal Real FFT](accelerate/in-place-functions-for-1d-multiple-signal-real-fft.md)