Fourier transform of a noisy signal

1. What is Fourier transform of noise?
2. Does Fourier transform remove noise?
3. How does noise affect FFT?
4. What is the Fourier transform of white noise?

What is Fourier transform of noise?

The Fourier transform can process out random noise and reveal the frequencies. For example, create a new signal, xnoise , by injecting Gaussian noise into the original signal, x . rng('default') xnoise = x + 2.5*randn(size(t)); Signal power as a function of frequency is a common metric used in signal processing.

Does Fourier transform remove noise?

Examples of such applications are canceling out electromagnetic conditions in radar measurements [5], echo suppression in audio processing [6], and 2D noise filter in image processing [7]. In the above, Fourier transform has proven to be functional and efficient tool for noise reduction.

How does noise affect FFT?

Contamination of signals by noise degrades the performance of fast Fourier transform (FFT) analysis of biological systems. Thus, we have developed simulation techniques to investigate the effects of noise on FFT computations.

What is the Fourier transform of white noise?

White noise vector

The power spectrum P of a random vector w can be defined as the expected value of the squared modulus of each coefficient of its Fourier transform W, that is, P_i = E(|W_i|²). Under that definition, a Gaussian white noise vector will have a perfectly flat power spectrum, with P_i = σ² for all i.