## What is decimation in time FFT algorithm?

The decimation-in-time (DIT) and the decimation-in-frequency (DIF) FFT algorithms are combined to introduce a new FFT algorithm, decimation-in-time-frequency (DITF) FFT algorithm, which reduces the number of real multiplications and additions.

**What is decimation in frequency FFT?**

The decimation-in-frequency FFT is a flow-graph reversal of the decimation-in-time FFT: it has the same twiddle factors (in reverse pattern) and the same operation counts. In a decimation-in-frequency radix-2 FFT as illustrated in Figure, the output is in bit-reversed order (hence “decimation-in-frequency”).

**Which FFT algorithm does MATLAB use?**

Discrete Fourier Transform of Vector.

### What is the time complexity of FFT?

FFT (Fast Fourier Transform) is particular implementation of DFT (Discrete Fourier Transform) and has computational complexity of O(N log(N) ), which is so far the best of all proposed Fourier transformations for discrete data. Most algorithms for DFT are O( N^2 ).

**What is decimation in time and frequency domain?**

Decimation in time DIT algorithm is used to calculate the DFT of a N-point sequence. The idea is to break the N-point sequence into two sequences, the DFTs of which can be obtained to give the DFT of the original N-point sequence.

**Why is FFT used in MATLAB?**

The fft function in MATLAB® uses a fast Fourier transform algorithm to compute the Fourier transform of data. Consider a sinusoidal signal x that is a function of time t with frequency components of 15 Hz and 20 Hz. Use a time vector sampled in increments of 1 50 of a second over a period of 10 seconds.

## Why is FFT faster than DFT?

FFT is based on divide and conquer algorithm where you divide the signal into two smaller signals, compute the DFT of the two smaller signals and join them to get the DFT of the larger signal. The order of complexity of DFT is O(n^2) while that of FFT is O(n. logn) hence, FFT is faster than DFT.

**How decimation in time DIT FFT is different from decimation in frequency DIT FFT?**

DITFFT stands for Decimation in Time Fast Fourier Transform and DIFFFT stands for Decimation in Frequency Fast Fourier Transform. In DITFFT, input is bit reversed while the output is in natural order, whereas in DIFFFT, input is in natural order while the output is in bit reversal order.