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This efficient use of memory is important for designing fast hardware to calculate the FFT. The term inplace computation is used to describe this memory usage.
Decimation in Time Sequence
In this structure, we represent all the points in binary format i.e. in 0 and 1. Then, we reverse those structures. The sequence we get after that is known as bit reversal sequence. This is also known as decimation in time sequence. Inplace computation of an eightpoint DFT is shown in a tabular format as shown below −
POINTS  BINARY FORMAT  REVERSAL  EQUIVALENT POINTS 

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 
Decimation in Frequency Sequence
Apart from time sequence, an Npoint sequence can also be represented in frequency. Let us take a fourpoint sequence to understand it better.
Let the sequence be
We will group two points into one group, initially. Mathematically, this sequence can be written as;
Now let us make one group of sequence number 0 to 3 and another group of sequence 4 to 7. Now, mathematically this can be shown as;
Let us replace n by r, where r = 0, 1 , 2….(N/21). Mathematically,
We take the first four points (x[0], x[1], x[2], x[3]) initially, and try to represent them mathematically as follows −
We can further break it into two more parts, which means instead of breaking them as 4point sequence, we can break them into 2point sequence.
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