# Sampling Analysis

#### Vikram50517

Joined Jan 4, 2020
39
Hello all! I have a doubt regarding sampling.when we sample below the nyquist frequency it is observed that in the freq domain,there exists a overlap between the signals,does it mean for the same freq 2 values of H(jw) exists?

#### MrAl

Joined Jun 17, 2014
8,479
Hello all! I have a doubt regarding sampling.when we sample below the nyquist frequency it is observed that in the freq domain,there exists a overlap between the signals,does it mean for the same freq 2 values of H(jw) exists?
You mean in the recovered signal?
I think you see a mix of two or more frequencies not really two separate if that's what you are talking about.
Consider what happens if you try to sample a 1kHz wave with maybe 100Hz not synced to the 1kHz. You would get a wave that changes shape over time that contains two or more frequency components i think. If it is synced i guess there is a change you would only see one frequency.
We could do some experiments maybe to see exactly what we get.

#### Vikram50517

Joined Jan 4, 2020
39
conidering the 3rd graph in the figure i have attested below there is an overlap between the 2 traingular sections.In the overlapped region it seems like for any freq there are 2 values of Xf(f) .how is that possible

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#### Papabravo

Joined Feb 24, 2006
16,830
The effect is called aliasing. What it means is the higher frequency components are folded back into the lower frequency range. They show up in the sampled data as lower frequency components that are not there in the original signal. This is why the first stage in a well designed digital filter includes an analog anti-aliasing filter to remove high frequency content that the digital filter cannot deal with.

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#### MrChips

Joined Oct 2, 2009
24,233
The triangles shown above are called Nyquist zones, zone 1, 2, 3, ... etc.

You want the low pass filter to remove all frequencies greater that what is in the first Nyquist zone.
(One can intentionally violate the Nyquist theorem to ones advantage. Under-sampling in order to extract signals in higher zones is done intentionally in digital radio, for example.)

Here is an example of what happens if the filter allows signals at frequencies above the Nyquist limit.

Suppose your sampling frequency is 1000Hz.
The Nyquist limit is 500Hz.

What happens if the low pass filter allows 600Hz through (i.e. a signal in zone 2)?
The reconstructed signal will be 1000 - 600 = 400Hz. This called alising.

900Hz becomes 1000 - 900 = 100Hz
1000Hz becomes 1000 - 1000 = 0 Hz
1100Hz becomes 1100 - 1000 = 100Hz

The third diagram shows what happens if the low-pass filter is wider than the first Nyquist zone. It allows signals from the 2nd zone to leak into the 1st zone. This results in aliasing - i.e. unintended frequencies that were not in the original signal.

#### Vikram50517

Joined Jan 4, 2020
39
Thank you all