Fourier transform

Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

Fourier transform

Postby nidhikapoor » Sat Jun 07, 2008 9:30 am

In oppenheim, its mentioned that

Ta[k] = sin(wt) / w

here sin(wt)/w is the envelope and a[k] defines the samples of the envelope. as the w tends to 0 the samples becomes closer enough and the summation turns to integral.
I didnt get this fact.

I got that the a[k] defines a signal where ..........a[0], a[1],.... are the samples but when we multiply it by T the amplitude of signal increases thats it. how come the samples a[k] becomes closer.

Please can anyone explain me this or send me some link where I can have more elaborate explaination of this topic.

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Re: Fourier transform

Postby newhere_andy » Thu Jun 12, 2008 2:05 pm

ok so when you're visualising you are fixing a[k].. you see a[k] will not be fixed.. It will be varying.. When they say they get closer... primarily what will happen is.. if you have 10 samples per period you might end up having 20 samples per period.. now if you see interms of k.. ir will still be 0 1 2 3 4 5 6.. etc.. but then a[1] might have been = sin (pi/4) but now it might be sin (pi/8).. hope that helped..

I know it might be easier if I had visually explained it.. let me know if this is not clear.. I will try to give a few diags..

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Fourier transform

Postby jiyamary » Mon Aug 18, 2014 5:05 pm

2 (SINE W)/W
2 (SINE 2W)/W
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