Howtosignalprocessing
- What is Fourier transform of autocorrelation?
- What are the disadvantages of FFT?
- What are the applications of autocorrelation function in signal processing?
- How accurate is FFT?
What is Fourier transform of autocorrelation?
R(τ)=∫∞−∞x(t)x∗(t−τ)dt. Statement − The autocorrelation property of Fourier transform states that the Fourier transform of the autocorrelation of a single in time domain is equal to the square of the modulus of its frequency spectrum.
What are the disadvantages of FFT?
A disadvantage associated with the FFT is the restricted range of waveform data that can be transformed and the need to apply a window weighting function (to be defined) to the waveform to compensate for spectral leakage (also to be defined). An alternative to the FFT is the discrete Fourier transform (DFT).
What are the applications of autocorrelation function in signal processing?
Autocorrelation is useful for finding repeating patterns in a signal, such as determining the presence of a periodic signal which has been buried under noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.
How accurate is FFT?
Fast Fourier transform (FFT)-based computations can be far more accurate than the slow transforms suggest. Discrete Fourier transforms computed through the FFT are far more accurate than slow transforms, and convolutions computed via FFT are far more accurate than the direct results.
