# 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 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,x,x,x,x,x,x,x . First, let’s group two points into one group. Mathematically, this sequence can be written as; 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; Let’s replace n by r, where r = 0, 1 , 2….(N/2-1). Mathematically, We are taking the first four points (x, x, x, x) initially and trying to represent them mathematically as shown below 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.

Digital Signal Processing Topics