Howtosignalprocessing
- How will you represent the Fourier series in complex form?
- What is the complex property of a Fourier series?
- What is complex Fourier transform?
How will you represent the Fourier series in complex form?
0.1 Fourier series in complex form
( t ) = ∑ n = - ∞ ∞ c n cn=12p∫p−pf(t)e−inπtpdt(n=0,±1,±2,…). p ∫ - p p f ( t ) e - i We may say that in (3), f(t) has been dissolved to sum of harmonics (elementary waves) cneinπtp with amplitudes cn corresponding the frequencies n .
What is the complex property of a Fourier series?
The complex Fourier series expresses the signal as a superposition of complex exponentials having frequencies: kT,k=....,−1,0,1,.... s(t)=∞∑k=−∞ckei2πktT. with. ck=12(ak−ibk)
What is complex Fourier transform?
The complex versions have a complex time domain signal and a complex frequency domain signal. The real versions have a real time domain signal and two real frequency domain signals. Both positive and negative frequencies are used in the complex cases, while only positive frequencies are used for the real transforms.
