Discrete Time Basis Functions

[@Mulkek]

Thanks, and it's so easy & simple!

[@iain_explains]

Glad you liked it!

[@mnada72]

6:36 Does that mean that the discrete fourier transform is just copies of continuous fourier transform at multiple 2pi intervals ?

[@iain_explains]

This might help: "How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?" kzbin.info/www/bejne/aJywhH-ndsd_oJY

[@ayushkumarrai1117]

I had a posted a doubt in your video of DTFT as to why the DTFT has to be periodic. Here you have answered it already! Can you please explain, why the repetition at every 2nπ? How did we get the value 2nπ?

[@iain_explains]

The 2π arises because the basis functions (cos and sin) have a period of 2π. In other words, cos(x)=cos(x+2π)=cos(x+2nπ) for any integer n.

[@ayushkumarrai1117]

@@iain_explains Sir, I was talking about any general signal. Like here in example cos function was taken, will the period of 2π DTFT hold for any arbitrary signal?

[@iain_explains]

Don't forget that all signals can be written as the sum of sin and cos functions (at different frequencies). That's what the Inverse Fourier Transform shows us.

[@ayushkumarrai1117]

@@iain_explains Ohh, now I got it sir. Thankyou!