[DSP] radix-2 DIT and DIF algorithms

[JJ91]

Homework Statement

Hi,

I literally can't see difference between DIT and DIF algorithms. Would be kind enough to explain a difference between two algorithms ?

Both algorithms have the same number of multiplications and additions for given signal:
[itex]\frac{N}{2}[/itex]log[itex]_{2}[/itex](N) - No. of Multiplications
Nlog[itex]_{2}[/itex](N) - No. of additions

Decimation in Time:

Decimation in Frequency:

The Attempt at a Solution

By looking into butterfly diagrams of both it can be seen that DIT starts from operation on pair of inputs ending on single multiplication at the last stage of FFT where is DIF starts from individual inputs computation ending on computation of pair of inputs.

In practice, what does that mean? How does that affect system?

 

[Valkarie]

DIT is a simpler algorithm since it has fewer stages and requires less memory as compared to DIF. This makes it easier to implement in hardware, which means it can operate faster. On the other hand, DIF requires more complex circuitry, so it may take more time to compute FFT. In terms of accuracy, both algorithms are accurate, but DIF has an advantage in that it offers better frequency resolution.