rsashwinkumar
Member level 4
I have a basic doubt regrading Continuous time Fourier Transform. Suppose a continuous signal has a band-limited CTFT spectrum (it exists only from say -Ωc to Ωc). Does that mean that if I pass it through a filter with a response such that it has a notch characteristic which selects only one frequency Ωb and Ωb<<Ωc, should a sinusoid at Ωc be expected at the output? Or in other words, if CTFT of a signal is non-zero for a particular frequency, does that mean the signal possess the corresponding sinusoidal frequency?
My doubt arose because of the following observation:
A sinc signal in time domain, will have a rectangular CTFT, and the CTFT is non-zero at Ω=0. So one may be tempted to conclude that average/DC value of sinc is non-zero, however the math suggests that sinc has a zero average value (as avg(sinc) = \[\lim_{T \to \infty} \frac{ 1}{ T}\int_{\frac{-T}{2}}^{\frac{T}{2}}sinc(t)\, dt = 0\]).
So can one infer the existence of a particular frequency component from Fourier Transform? Or how to interpret the Continuous Time Fourier Transform..
Plz help me out...
My doubt arose because of the following observation:
A sinc signal in time domain, will have a rectangular CTFT, and the CTFT is non-zero at Ω=0. So one may be tempted to conclude that average/DC value of sinc is non-zero, however the math suggests that sinc has a zero average value (as avg(sinc) = \[\lim_{T \to \infty} \frac{ 1}{ T}\int_{\frac{-T}{2}}^{\frac{T}{2}}sinc(t)\, dt = 0\]).
So can one infer the existence of a particular frequency component from Fourier Transform? Or how to interpret the Continuous Time Fourier Transform..
Plz help me out...