Period and Aliasing Problems

Thread Starter

josh007

Joined Sep 20, 2015
43
Good day All,

I need your valued precious advice and help once again, in correcting my tutorial homework examples.

Please can you check my work if I am correct or advice where I am going wrong.

gracias

Q1)

If the signal x(t)=4cos(200πt) is sampled at 500 Hz, determine the signal x(n).

What is the period of the sampled signal?

MY ANSWER:

x(t)=4cos((200/500)πt)

so my signal x(n) = 4cos((2/5)πt)


P = 2π/w


Where w is the angular velocity = 2π/5


P = 2π/(2π/5) = 5 units


So Period is 5 units



Q2)

Determine the minimum sampling rate to avoid aliasing for the signal x(t)=20cos(400πt)+10cos(20πt).

MY ANSWER:

I will take the highest frequency to avoid aliasing.


So P = 2π/w = 2π/400π = 1/200


Therefore f= 1/T = 1/(1/200) = 200hz


To avoid aliasing fx2 = 400hz
 

WBahn

Joined Mar 31, 2012
26,326
Looks good, except that sampling rates should not be given in Hz (though they often are), since 1 Hz is one cycle per second. Instead, the units should be Sa/s (samples per second).
 

Thread Starter

josh007

Joined Sep 20, 2015
43
Looks good, except that sampling rates should not be given in Hz (though they often are), since 1 Hz is one cycle per second. Instead, the units should be Sa/s (samples per second).
Fantastic, much appreciation WBahn, I will take note of this. You are correct I read in my text book about the Sa/s but completely forgot about it.

Gracias
 

crutschow

Joined Mar 14, 2008
25,695
Looks good, except that sampling rates should not be given in Hz (though they often are), since 1 Hz is one cycle per second. Instead, the units should be Sa/s (samples per second).
upload_2016-7-4_1-43-59.png
upload_2016-7-4_1-45-41.png

So I think it's okay to refer to a sample rate as a sample frequency in Hertz. :)
 

DickCappels

Joined Aug 21, 2008
6,661
Alternative definitions are in common use. e.g.: What is the spatial frequency of this bar pattern?
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