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The concept of Fast Fourier Transform (FFT) is quite a critical and complicated one. It involves complex mathematical algorithms those are to be understood very clearly. An FFT calculatesthe conversion of signal rapidly by factorizing Discrete Fourier Transform (DFT) matrix into a product of sparse features. The process finally reduces complexity of calculating DTF from O(n2).
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Discrete Fourier Transform – Properties
Let’s have a look at the various properties of DFT.
- Time Shifting
- Linearity
- Frequency Shifting
- Frequency differentiation
- Time Reversal
- Differencing
- Parseval’s Relation
- Convolution Theorems
An in-depth idea of the above points will be discussed in our Discrete Fourier Transform, Fast Fourier Transform (FFT) assignment help. Each of the properties has an equation against them for exact and proper definitions.
To mention a disadvantage of DFT technique, it requires huge power for processing as every harmonic has to be calculated separately. But it gives exact answers if processing power is available.
FFT is faster:
Fast Fourier Transform technique is faster than DFT as its name implies. It calculates at a speed 100 times more. If we consider taking a waveform of 1024 samples as N, then it calculates the value of N2 but an FFT calculates Nlog2(N).
Experts drag the conclusion that although the speed of FFT is higher than DFT, yet practically, DFT gives more accurate results with proper power application. The performance is thus, better. Many more comparisons are there to differentiate the two techniques, all widely discussed in Discrete Fourier Transform, Fast Fourier Transform (FFT) homework help.
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