# Documentation

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# bitrevorder

Permute data into bit-reversed order

## Syntax

```y = bitrevorder(x) [y,i] = bitrevorder(x) ```

## Description

`bitrevorder` is useful for pre-arranging filter coefficients so that bit-reversed ordering does not have to be performed as part of an `fft` or inverse FFT (`ifft`) computation. This can improve run-time efficiency for external applications or for Simulink® blockset models. Both MATLAB® `fft` and `ifft` functions process linear input and output.

### Note

Using `bitrevorder` is equivalent to using `digitrevorder` with radix base 2.

`y = bitrevorder(x)` returns the input data in bit-reversed order in vector or matrix `y`. The length of `x` must be an integer power of 2. If `x` is a matrix, the bit-reversal occurs on the first dimension of `x` with size greater than 1. `y` is the same size as `x`.

`[y,i] = bitrevorder(x)` returns the bit-reversed vector or matrix `y` and the bit-reversed indices `i`, such that `y = x(i)`. Recall that MATLAB matrices use 1-based indexing, so the first index of `y` will be 1, not 0.

The following table shows the numbers 0 through 7, the corresponding bits, and the bit-reversed numbers.

Linear Index

Bits

Bit- Reversed

Bit-Reversed Index

0

000

000

0

1

001

100

4

2

010

010

2

3

011

110

6

4

100

001

1

5

101

101

5

6

110

011

3

7

111

111

7

## Examples

collapse all

Create a column vector and obtain its bit-reversed version. Verify by displaying the binary representation explicitly.

```x = (0:15)'; v = bitrevorder(x); x_bin = dec2bin(x); v_bin = dec2bin(v); T = table(x,x_bin,v,v_bin)```
```T=16x4 table null x x_bin v v_bin __ _____ __ _____ 0 0000 0 0000 1 0001 8 1000 2 0010 4 0100 3 0011 12 1100 4 0100 2 0010 5 0101 10 1010 6 0110 6 0110 7 0111 14 1110 8 1000 1 0001 9 1001 9 1001 10 1010 5 0101 11 1011 13 1101 12 1100 3 0011 13 1101 11 1011 14 1110 7 0111 15 1111 15 1111 ```