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# digitrevorder

Permute input into digit-reversed order

## Syntax

y=digitrevorder(x,r)
[y,i]=digitrevorder(x,r)

## Description

digitrevorder is useful for pre-ordering a vector of filter coefficients for use in frequency-domain filtering algorithms, in which the fft and ifft transforms are computed without digit-reversed ordering for improved run-time efficiency.

y = digitrevorder(x,r) returns the input data in digit-reversed order in vector or matrix y. The digit-reversal is computed using the number system base (radix base) r, which can be any integer from 2 to 36. The length of x must be an integer power of r. If x is a matrix, the digit reversal occurs on the first dimension of x with size greater than 1. y is the same size as x.

[y,i] = digitrevorder(x,r) returns the digit-reversed vector or matrix y and the digit-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 15, the corresponding digits and the digit-reversed numbers using radix base-4. The corresponding radix base-2 bits and bit-reversed indices are also shown.

Linear Index

Base-4 Digits

Digit- Reversed

Digit- Reversed Index

Base-2 Bits

Base-2 Reversed (bitrevorder)

Bit- Reversed Index

0

00

00

0

0000

0000

0

1

01

10

4

0001

1000

8

2

02

20

8

0010

0100

4

3

03

30

12

0011

1100

12

4

10

01

1

0100

0010

2

5

11

11

5

0101

1010

10

6

12

21

9

0110

0110

6

7

13

31

13

0111

1110

14

8

20

02

2

1000

0001

1

9

21

12

6

1001

1001

9

10

22

22

10

1010

0101

5

11

23

32

14

1011

1101

13

12

30

03

3

1100

0011

3

13

31

13

7

1101

1011

11

14

32

23

11

1110

0111

7

15

33

33

15

1111

1111

15

## Examples

Obtain the digit-reversed, radix base-3 ordered output of a vector containing 9 values:

```x=[0:8]';                % Create a column vector
[x,digitrevorder(x,3)]
% ans =
%
%    0     0
%    1     3
%    2     6
%    3     1
%    4     4
%    5     7
%    6     2
%    7     5
%    8     8
```