energy of a sinc signal
in [DSP]
|
From: bharat pathak on 4 May 2008 22:43 what is the value of the energy for the following sinc signal. x(t) = sin(2*pi*f*t)/(pi*t);
From: cincydsp on 4 May 2008 23:29 On May 4, 10:43 pm, "bharat pathak" <bha...(a)arithos.com> wrote: > what is the value of the energy for the following > sinc signal. > > x(t) = sin(2*pi*f*t)/(pi*t); Use Parseval's theorem. The amount of energy in the time-domain representation of a signal must be equal to the amount of energy in its frequency-domain representation. A sinc transforms to a rectangle in the frequency domain. Once you get the scaling right (factors of T = 1/f, etc.), you should get your answer easily. Jason
From: rajesh on 4 May 2008 23:32 On May 5, 7:43 am, "bharat pathak" <bha...(a)arithos.com> wrote: > what is the value of the energy for the following > sinc signal. > > x(t) = sin(2*pi*f*t)/(pi*t); Hi Bharat, I guess the fourier transform of the mentioned sinc function is is rectangular pulse. So instead of going for a definite integral and its convergence we can compute the energy in frequency domain.(Parseval relation), where its just an area of a rectangle. Cant remember the formula for the width and height of the rectangle. is it 1/f ? in that case the asnwer is 1/f or is it 2/f?
From: robert bristow-johnson on 5 May 2008 00:14 On May 4, 11:32 pm, rajesh <getrajes...(a)gmail.com> wrote: > On May 5, 7:43 am, "bharat pathak" <bha...(a)arithos.com> wrote: > > > what is the value of the energy for the following > > sinc signal. > > > x(t) = sin(2*pi*f*t)/(pi*t); > > Hi Bharat, > > I guess the fourier transform of the mentioned sinc > function is is rectangular pulse. > So instead of going for a definite integral and its > convergence we can compute the energy > in frequency domain.(Parseval relation), where its just > an area of a rectangle. > > Cant remember the formula for the width and height of > the rectangle. is it 1/f ? > in that case the asnwer is 1/f or is it 2/f? This is why, in my opinion, when doing continuous-time signal processing, the "unitary Fourier Transform" and its inverse (both with "j 2 pi f" in the exponents and no scaling constant outside the integral) is the best way to do it. Parseval's Theorem, convolution theorem, duality, and many other things are just easier. the F.T. of the unit sinc function: x(t) = sinc(t) = sin(pi t)/(pi t) is the unit width rectangular function: X(f) = rect(f) { 1 |f| < 1/2 = { { 0 |f| > 1/2 i commit that to memory (along with the prototype gaussian pulse function) and the rest of the scaling can be done readily. so for x(t) = sin(2*pi*f0*t)/(pi*t) which is x(t) = (2*f0) * sin(2*pi*f0*t)/(2*f0*pi*t) the area of the F.T. must be 2*f0 and the frequency gets scaled by 1/ (2*f0), so it has F.T. of X(f) = rect( f/(2*f0) ) the energy is the area of the square of the rect() or simply 2*f0. r b-j
From: bharat pathak on 5 May 2008 01:38
Thanks r b-j Regards Bharat |