Howtosignalprocessing
- What is the Fourier transform of the autocorrelation function?
- What are the similarities and differences between Fourier series and Fourier transforms?
- What is the main difference between Fourier series and Fourier transform?
- What is the difference between Fourier transform and Laplace transform?
What is the Fourier transform of the autocorrelation function?
It can be shown that the Fourier Transform of the auto-correlation of a function is the square of its Fourier Transform, i.e. its power spectrum. The cross-correlation of two functions f(x) and g(x) is defined by. Rx(u) ≡ ∫ ∞
What are the similarities and differences between Fourier series and Fourier transforms?
Fourier series is a technique of decomposing a periodic signal into a sum of sine and cosine terms. Fourier Transform is a mathematical operation for converting a signal from time domain into its frequency domain. Fourier series can be applied to periodic signals only.
What is the main difference between Fourier series and Fourier transform?
The difference between the Fourier transform and the Fourier series is that the Fourier transform is applicable for non-periodic signals, while the Fourier series is applicable to periodic signals.
What is the difference between Fourier transform and Laplace transform?
What is the distinction between the Laplace transform and the Fourier series? The Laplace transform converts a signal to a complex plane. The Fourier transform transforms the same signal into the jw plane and is a subset of the Laplace transform in which the real part is 0.
