signal sampling and recovery

Discussion in 'Homework Help' started by jut, Nov 16, 2009.

  1. jut

    Thread Starter Senior Member

    Aug 25, 2007
    224
    2
    The signal x(t) = cos (14*pi*t) is sampled at a sampling interval of T = 0.1 seconds. Can we recover the signal from its samples (why or why not).


    I attached my attempt at a solution.

    What I did was this: I did a fourier transform on the signal, X(w), which resulted in two delta functions: one located at -14pi, the other at 14pi. Now, the fourier transform of the sampled signal, Xs(w) equals X(w) plus X(w) shifted by integer multiples of n*2*pi/Ts which equals 20*pi.

    From my plot of Xs(w), there are delta functions interspersed to the left and right of the original X(w). I don't know if the original signal can be recovered with an anti-aliasing filter.
     
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  2. Papabravo

    Expert

    Feb 24, 2006
    10,152
    1,794
    Lotta work -- and completely unnecessary.
    Code ( (Unknown Language)):
    1.  
    2. 2πf = 14π
    3. f=7 Hz.
    4. fs(minimum) = 14 Hz.
    5. 1/14 = 71.4 milliseconds
    6.  
    The sampling frequency must be twice the highest frequency component. A sampling frequency of 10 Hz., corresponding to a sampling period of 100 milliseconds, just won't make it.
     
  3. jut

    Thread Starter Senior Member

    Aug 25, 2007
    224
    2
    that's a whole lot easier, ugh. :(

    thanks for the help.
     
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