# Sampling and aliasing

#### naickej4

Joined Jul 12, 2015
206
Hello,
I have a silly question to ask, just to refresh my knowledge on Sampling in DSP. Please can someone check if what I am doing is correct and correct me along the way. I am preparing for a test which covers old work that was done at the beginning of the year and I have forgotten some important concepts.

Question:
A 100 Hz signal is sampled at 250 Hz. Discuss if aliasing has occurred and how many periods of the signal is required to obtain one period of the sampled signal?

Aliasing will not occur since the sampled frequency (250 Hz) is more than twice the maximum frequency (100 Hz)
100/250 = 2/5 so the period is 5
The Period of 100 Hz is 1/100
So I took (5/(1/100)) which is 500

thank you.

#### crutschow

Joined Mar 14, 2008
34,681
I'm not sure I understand the second part of the question.
What is meant by "obtain one period of the sampled signal"?

#### MrAl

Joined Jun 17, 2014
11,565
Hi,

Sounds like it means when do the two signals becomes aligned again if they both start out at zero degrees.
Or, how many periods is required to effectively recreate the original signal.

#### RBR1317

Joined Nov 13, 2010
715
The Nyquist rate for a 100 Hz signal is 200 samples/sec. Since the sampling rate here exceeds the Nyquist rate, there will be no aliasing error.

The answer to the second half of the question must obviously be 'one' since the "signal" and the "sampled signal" are the same; however, it is unclear just what principle is meant to be demonstrated here - unless it is that the 'signal' and the 'sampled signal' are the same signal!

#### naickej4

Joined Jul 12, 2015
206
Hi All. Thanks. I'm also confused now. I copied this question from a past 2015 exam paper. Unfortunately they have no memo so I can't check the answer.
Thank you

#### MrAl

Joined Jun 17, 2014
11,565
Hi,

Yes i also have to wonder if they are allowing sub cycle answers, because the sampling frequency is higher than the min rate. They might want to round up to the nearest whole cycle though if we cant say that the sampling starts at 0 degrees. So i can see them wanting either one full cycle or the fraction of that where we get the second sample. I'd be more inclined to think it would be the full cycle though.

Shown in the attachment are two waves, one at 100Hz and one at 250Hz. If we say that we sample at 0 degees of the 250Hz wave then we get the required information at less than one full cycle. But because sampling is almost never aligned with the signal, we probably have to assume that the sampling can occur at any angle, so we would need a full cycle to ensure that we get enough information. On the other hand, no matter where we sample (what angle) we always only need a partial cycle to get the required information. The question itself however does not seem to suggest that partial cycles are allowed though.

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#### naickej4

Joined Jul 12, 2015
206
Hi Sir. I'm not too sure. But I will email the lecturer on moday and find out. The test is on Thursday though. I hate to have ambiguous type of questions for a test.

#### naickej4

Joined Jul 12, 2015
206
Oh wait in the heading of the exam paper its says. If you have the opinion that insufficient information is supplied for you to answer a particular question. Make a realistic assumption, motivate it and then answer the question.

#### MrAl

Joined Jun 17, 2014
11,565
Hi,

Oh very good then. In that case, what do you think would be a correct answer?

#### naickej4

Joined Jul 12, 2015
206
Hi Sir. Is the answer 5/2?

Thank you

#### MrAl

Joined Jun 17, 2014
11,565
Hi,

Well what is your reasoning behind that result?

#### naickej4

Joined Jul 12, 2015
206
Hi
Hi,

Well what is your reasoning behind that result?
Hi Sir.
Since100/250 = 2/5 so the
period is is 1/frequency.
Then its 5/2
Thank you