bitrevorder

Permute data into bit-reversed order

Description

example

y = bitrevorder(x) returns the input data in bit-reversed order.

[y,i] = bitrevorder(x) also returns the bit-reversed indices, i, such that y = x(i).

Examples

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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=16×4 table
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

Input Arguments

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Input data, specified as a vector or matrix. The length or number of rows 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.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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

Bit-reversed indices, returned as a vector or matrix such that y = x(i). MATLAB® matrices use 1-based indexing, so the first index of y is 1, not 0.

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Bit-Reversed Ordering

bitrevorder is useful for prearranging filter coefficients so that bit-reversed ordering does not have to be performed as part of an fft or ifft computation.

Bit-reversed ordering 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.

This 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