Digital signal processing

Discussion in 'Homework Help' started by vvkannan, Jan 26, 2009.

  1. vvkannan

    Thread Starter Active Member

    Aug 9, 2008
    138
    11
    Hello all,

    I have this subject this semester.Here under the topic ' Properties of discrete time sinusoidal signal' my text states this
    "The frequency of oscillation of discrete-time sinusoidal sequence increases as 'w' increases from 0 to pi.If 'w' is increased from pi to 2(pi) then the frequency of oscillation decreases"
    x(n) = cos (1.8PI n) where w=1.8 pi is an example it says.
    I cant understand this.
    how can frequency decrease when 'w' increase?
    Thank you
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    Aliasing. The higher frequency sampled at a fixed rate is aliased into the lower frequency. They are in every sense indsitinguishable.
     
  3. GirishC

    Active Member

    Jan 23, 2009
    58
    0
    Hi

    In case of DSP, you sample any given input, in this case a sinusoidal input. Based on your sampling frequency (which is constant) you get samples i.e. magnitude and phase angle. If you map these points you will have these plotted in circle. so if you change your angle from 0 to PI you get magnitude change from 1 to -1 as you traverse further from PI to 2PI it again comes back to 1. And you feel that the frequency component lies in the 0 to PI range (called as alising). And hence you get subtraction.

    This phenomena can be physically seen, when you loot at moving wheel of car, at some point you see that wheel is either stationary or rotating in reverse direction. It is the same phenomena described mathematically.

    I hope, its not confusing...
     
  4. vvkannan

    Thread Starter Active Member

    Aug 9, 2008
    138
    11
    Thank you papabravo and girishc.
    it's clearer than before,but iam having some doubts still

    yes if a circle is obtained then it can be considered as an increase and then decrease.but i cant understand ur 3rd line here and moreover i find it difficult to understand ur example that is i find it difficult to relate the concept with that one.
    maybe ur advanced.
    iam a bit clearer now
    thanks again
     
  5. GirishC

    Active Member

    Jan 23, 2009
    58
    0
    Simply consider you have a sinusoid given by

    v = V*cos(w*t)

    where
    V = magnitude
    v = instantaneous value
    w = frequency in rad/sec
    t = time

    Now, w is a vector which moves in anticlockwise direction. At each value of wt, you get v. You get maximum V at 0 & PI degrees and zero V at PI/2 & -PI/2.

    All sinusoidal signals are phasors so even the angle is increased linearly, signal will keep oscillating.

    You need to keep above theory in mind, when you read my third line. Probably will clear your understanding more.
     
  6. vvkannan

    Thread Starter Active Member

    Aug 9, 2008
    138
    11
    I understand that the sinusoidal signals can be represented as phasors and so 'w' can be considered to increase linearly but what i cant understand here is how the frequency decreases during this increase of 'w'.
    Imagining it as a circle really helped but the only doubt i have now is what i have stated above.
    Thank you helping me out
     
  7. GirishC

    Active Member

    Jan 23, 2009
    58
    0
    After PI, you can not distinguish between higher frequency as it coincides with lower frequency. So you tend to assume it as a lower frequency. Compare with car wheel example.
     
  8. vvkannan

    Thread Starter Active Member

    Aug 9, 2008
    138
    11
    so we cannot 'distinguish' between the higher and lower frequency of 'w' forming a circular pattern and thats y it appears to be dercreasing.right?
    thank you very much .I am a lot clearer now
     
  9. GirishC

    Active Member

    Jan 23, 2009
    58
    0
    Yes that's true...that's the limitation of in discrete domain not observed in continuous domain.
     
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