CE 5310 Lecture Notes - Lecture 4: Bandlimiting, Negative Frequency, Discrete-Time Fourier Transform
Document Summary
Fourier transform (ft) is a mathematical tool to transform time domain signal to frequency domain. It is widely used in telecommunication and signal processing. For a periodic signal f(t) with period t1, if it satisfies dirichlet condition, it can be expanded as f t a. 0 f t dt is the dc component, a n. 1 t) dt is the cosine component, and b n. 1 where j is the imaginary unit, f(t) can be expanded in exponential series shown in equation 3. 2 jb n where na and nb are even and odd functions of n and let f(0)= 0a , f(t) can be written as f t n. 1 dt is usually complex function of n. the absolute value of. 1 can describe the frequency spectrum (representation of signal in frequency domain) of periodic signal f(t). 1 dt f t e j t dt (6) then the fourier series also becomes f t.
