1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sampling a continuous-time signal, aliasing/Nyquist

  1. Oct 24, 2016 #1
    1. The problem statement, all variables and given/known data
    The analog signal x(t) = cos(2pi f t) is sampled at a rate of 1 kHz, using ideal
    impulse sampling, to obtain the sampled signal x^(s)(t). The sampled signal is then sent through an ideal
    lowpass filter with transfer function H(2pi f ) = 0.001 rect (0.001 f ).
    (a) If f =1.01kHz, what is the output frequency from the filter? Is there aliasing or not?
    (b) If f = 0.99kHz, what is the output frequency from the filter? Is there aliasing or not?
    (c) If f = 0.49kHz, what is the output frequency from the filter? Is there aliasing or not?

    2. Relevant equations
    To perfectly reconstruct a signal, we need: sampling rate > 2*signal frequency

    3. The attempt at a solution
    I think these are correct, not 100% sure though:
    (a)
    aliasing occurs, as 1.00 kHz !> 2 × 1.01 kHz
    fout = 1.01 kHz – n × 1.00 kHz = 1.01 kHz – 1 × 1.00 kHz = 0.01 kHz

    (b)
    aliasing occurs, as 1.00 kHz !> 2 × 0.99 kHz
    fout = 0.99 kHz – n × 1.00 kHz = 0.99 kHz – 1.00 kHz = - 0.01 kHz

    (c)
    aliasing does not occur, as 1.00 kHz > 2 × 0.49 kHz
    fout = 0.49 kHz
     
  2. jcsd
  3. Oct 26, 2016 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Not sure I understand this terminology. What really is the ideal low-pass cutoff frequency? Is it really a function of input frequency f? Do you have to divide by 2π? Etc. ???

    I don't know your method, and as I say I'm not sure what your cutoff filter really looks like, but it basically seems to work.

    Just FYI I first determine the cutoff frequency of the low-pass filter = f0, the I take the sampling frequency fs and my input frequency f and find spectral components:

    f, |fs - f|, fs + f, |2fs - f|, 2fs + f, ...

    and then compare each component against the cutoff frequency f0.
    The only unaliased signal is at f so anything below f0 that is a mix of f and fs is an aliased component.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted