digitrevorder

Permute input into digit-reversed order

Syntax

y = digitrevorder(x,r)

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

Description

y = digitrevorder(x,r) returns the input data x in digit-reversed order. The digit-reversal is computed using the number system base (radix base) r.

[y,i] = digitrevorder(x,r) returns the digit-reversed input data and digit-reversed indices, such that y = x(i).

Examples

Base-3 Digit-Reversed Order

Obtain the digit-reversed, radix base-3 ordered output of a vector containing 9 values. Obtain the same result by converting to base 3 and reversing the digits.

x = (0:8)';

y = digitrevorder(x,3);

c1 = dec2base(x,3);
c2 = fliplr(c1);
c3 = base2dec(c2,3);

T = table(x,y,c1,c2,c3)

T=9×5 table
    x    y    c1    c2    c3
    _    _    __    __    __

    0    0    00    00    0 
    1    3    01    10    3 
    2    6    02    20    6 
    3    1    10    01    1 
    4    4    11    11    4 
    5    7    12    21    7 
    6    2    20    02    2 
    7    5    21    12    5 
    8    8    22    22    8 

Input Arguments

x — Input data

vector | matrix

Input data, specified as a vector or matrix. 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.

r — Radix base

integer

Radix base, specified as an integer in the range [2, 36].

Output Arguments

y — Digit-reversed data

vector | matrix

Digit-reversed data, returned as a vector or matrix. y is the same size as x.

i — Digit-reversed indices

vector | matrix

Digit-reversed indices, returned as a vector or matrix.

Note

MATLAB^® matrices use 1-based indexing, so the first index of y will be 1, not 0.

More About

Digit-Reversed Numbers

This 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

Tips

• The digitrevorder function 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.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a