DSP In-Place Computation - Digital Signal Processing

What is the use of DSP In-Place Computation?

Efficient usage of memory is very essential to design fast hardware for calculating the FFT. The term in-place computation is used for describing this memory usage.

Decimation in Time Sequence

In this structure, all the points are represented in binary format i.e. in 0 and 1 and those structures are then reversed. The sequence we get after that is known as bit reversal sequence. This is also known as decimation in time sequence. In-place computation of an eight-point 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_time_sequence.jpg

Decimation in Frequency Sequence

Apart from time sequence, an N-point sequence is also represented in frequency. Let’s take a four-point sequence for understanding it better.

Let the sequence be x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7] . First, let’s group two points into one group. Mathematically, this sequence can be written as;

formula.PNG

Now let’s make one group of sequence number 0 to 3 and another group of sequence 4 to 7. Now, mathematically this can be represented as;

formula.PNG

Let’s replace n by r, where r = 0, 1 , 2….(N/2-1). Mathematically,

formula.PNG

We are taking the first four points (x[0], x[1], x[2], x[3]) initially and trying to represent them mathematically as shown below

formula.PNG

It can be further breaked into two more parts, which means instead of breaking them as 4-point sequence, we can break them into 2-point sequence.

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