digitrevorder

Rearranges the digits of the input data in reverse order.

Library

EngeeDSP

Syntax

Function call

y, i = digitrevorder(x, r) — returns the digits of the input data x in reverse order and their indexes i So that y = x(i). The numbers are rearranged using the base of the numeral system. r.

Arguments

Input arguments

# x — input data

+ vector | the matrix

Details

Input data specified as a vector or matrix. Length x must be an integer power of a number r. If x — the matrix, then the numbers are rearranged in the first dimension x, the size of which is larger 1.

# r is the base of the number system

+ an integer

Details

The base of the number system, specified as an integer in the range [2, 36].

Output arguments

# y — the digits of the input data in reverse order

+ vector | the matrix

Details

The digits of the input data are in reverse order, returned as a vector or matrix. Argument y has the same size as x.

# i — indexes of rearranged digits

+ vector | the matrix

Details

The indexes of the rearranged digits returned as a vector or matrix. Indexing starts with 1.

Examples

The numbers are in reverse order in the number system with base 3

Details

Let’s set an input vector of 9 values. We get a vector containing the numbers in reverse order in the base number system. 3 and their indexes.

import EngeeDSP.Functions: digitrevorder

x = (0:8)'

y, i = digitrevorder(x,3)

println("x\ty\tj")
println("__________________")
for j in 1:length(x)
    println(x[j],"\t",y[j],"\t", i[j])
end

x	y	j
__________________
0	0	1
1	3	4
2	6	7
3	1	2
4	4	5
5	7	8
6	2	3
7	5	6
8	8	9

Additional Info

The numbers are in reverse order

Details

This table shows the numbers from 0 before 15, their corresponding numbers and numbers in reverse order in the base number system 4. The corresponding bits in the base number system are also shown. 2 and the corresponding indexes.

Linear index	Base numbers `4`	The numbers are in reverse order	Indexes of numbers in reverse order	Base bits `2`	The bits are in reverse order	The bit indexes are in reverse order
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

Recommendations

Function digitrevorder it is useful for pre-ordering a vector of filter coefficients for use in frequency domain filtering algorithms in which transformations fft and ifft they are calculated without the reverse order of digits to increase the efficiency of execution.