Why is Windowing Needed in Digital Signal Processing?

[@kkgt6591]

Can you please show the circuits which create these window functions?

[@Pedro-rz5dc]

As DFT is a discrete algorithm, with implementation in digital systems, the "circuits" that implement them are rather "code circutis",i.e, code that implement each windowing function. For instance, if you search for DSP libraries there are a plethora of implementations (a lot calling C functions with math.h standard library geometric functions). At least, that is my understanding.

[@lohikarhu734]

Really nice 👍

[@iain_explains]

Thank you! Cheers!

[@lohikarhu734]

It reminds me of the picture that many people have of Nyquist... They don't understand that the theorom only holds for a continuous waveform, as, otherwise, you are "windowing" the sinusoid by some finite period. I think.

[@jasminnadic2103]

Thank you, a more general question. When I have the signal given in the form y(t)=cos(2×pi×t-phi), how do I know that we are in the frequency domain or time domain? I assume we are in time here because "y(t)". Because we have f and t in the equation and sometimes we have just t in the equation e.g. y(t)=t×s(t) - here it is clear, we have just t in the equation. Thanks.

[@iain_explains]

You don’t have f in the equation you wrote! Only t. So it’s the time domain.

[@jasminnadic2103]

@iain_explains I am sorry, I mean y(t)=cos(2×pi×f×t-phi). Is f here a fixed value? Thank you.

[@iain_explains]

Yes, when people write the equation the way you have now, they are generally referring to a sinusoidal carrier waveform in a communication system, where the "f" in your equation is most commonly written "f_c", which refers to the carrier frequency. It's the specific frequency given by the oscillating crystal.

[@pitmaler4439]

When I have that DFT vector with the entries at 1 and 7, what is the equation to get to the frequency f=1/p (by calculation)? Thanks

[@iain_explains]

This video should help to explain it: "How does the Discrete Fourier Transform DFT relate to Real Frequencies?" kzbin.info/www/bejne/pnqpq2tqpM9smaM