Aliasing and the Sampling Theorem Simplified

A presentation of aliasing, the sampling theorem, and the Fourier transform representation of a sampled signal that does not make extensive use of Fourier transform properties and impulse trains, but instead relies on the relationship between continuous- and discrete-time frequency and the non uniqueness of discrete-time sinusoids.

[alisaaeddin]

Man this was not at all simple, but it was great explained. I had to look at other videos to understand this one

[PankajSingh-dcqp]

@ 8:38 W is not the nyquist frequency. The actual sampling frequency, w_s, is commonly referred to as the Nyquist frequency.

[alienbash]

Thanks a lot for this video! One question concerning the slides at 18:40 violating the sampling theorem means that we lose uniqueness of the FT of the signal, but what does that mean for a concrete simulation? I'm thinking e.g. about elelectromagnetic waves (electric field vector) on a finite grid, which has frequencies greater than the niquisit sampling rate (given by the finite grid resolution). Would that violation mean, that those waves can't be correct, i.e. there may be some "pseudo reflections" going on due to this violation?

[payamm]

Hi, thank you for your videos. I have however some newbe questions. Why would you shift the FT of sampled signal to the origin. what is the pupose of that? I mean the original signal has it's componentes in different intervall and you move them on purpose to the origin just becouse it's between -pi and pi but the original signal is not between these two.  thanks in advance

[allsignalprocessing]

Because e^{j 2pi n} = 1 for any integer n. Thus, in discrete time e^{j (om + 2pi) n} = e^{j om n}. This doesn't happen in continuous time because t is not restricted to be an integer.

[TerranIV]

Slide 6 is a bit confusing as you state that the "bandwidth" is 10pi. I think this is because you are using W to represent Nyquist frequency instead of Nyquist rate. The cutoff frequency is 10pi, but the bandwidth is 20pi. Correct?

[qieeebranch]

There may be an error on the last slide. The amplitude of X(e^jw) should be 8, right? For the example with the sampling interval of T = 1/8.

[joebonar]

I'm getting tripped up on the notation. I thought the Continuous time Fourier Transform was in terms of (w {lower case omega}) and the DTFT was in terms of Omega, is that "right" or is the notation in the video the proper way?

[MrForeverBlues]

How do we solve for this?
Given that y(t)=x(t)[cos(3*pi*t)+sin(10*pi*t)], find the Wmax and for which x(t) can be reconstructed from y(t). Please specify the system?
Can you please guide me step by step?

[SandeepAitha]

why discrete time sinusoids are unique for a 2pi interval of omega?
and what is happening for continous time signal?