# Is Oversampling a Signal Same as Discretizing the Signal?

I am confused about the new terminology 'oversampling' I have encountered very recently. To explain it better, I am going to use numerical examples. Now let's assume I am using a BPSK modulator and my symbol period is 1 second. To digitize and process this using MATLAB or Python, what I was doing was to discretize the signal with 100. (Using np.repeat() or repmat to information bit sequence). My questions are:

1) Is this value (100) the oversampling factor?

2) Is this discretization value of mine, is the ratio between symbol duration times sampling frequency of the system ?

3) If the ratio that I mentioned earlier is not what oversampling is, can you explain or give me links for some kind of explanation? ( I found a lot about it but it made me even more confused due to the fact people are using upsampling and oversampling interchangeably, which I think is totally wrong)

• what I was doing was to discretize the signal with 100. 100 what? – MBaz Jun 17 '18 at 0:49
• Lets say I have information bits a_n=[1,-1]. By discretizing it with 100, I make it [1,1,1,1,1,1,1....,-1,-1,-1,-1] each symbol 100 times. – Avio Jun 17 '18 at 8:08
• @Avio, Replicating the Symbols isn't Oversampling. See my answer below. – Royi Jun 17 '18 at 8:27

Oversampling is the case the rate the data is sampled is higher than required by the data Bandwidth and Nyquist Shannon Sampling Theorem.
It has many good properties regarding the processing yet it also generate some issues (Like coloring the quantization noise).

1. In BPSK the symbol is the phase range of modulated signal (Sign). By using repmat() you indeed oversmapled the data (Symbols) yet not the modulated signal. What you needed to do is creating a grid where you sample the modulated signal. So if the the modulated signal has a frequency $f$ than for 100 oversampling rate you should sample at ${F}_{s} = 100 \cdot 2 \cdot f$.

2. What you did is replication of the symbol. Not higher sampling rate unless you imitate the effect of oversampling after Symbol inference.

3. In order to see the effect of oversmapling by factor of $100$ generate the modulated signal over a grid where $\Delta T = \frac{1}{100 \cdot 2 \cdot f}$ with $f$ being the modulating signal frequency.

Regarding your question in the title.
The process of sampling data is basically discretizing data over 2 grids:

1. The Time Grid
Basically sampling the continuous data in specific times. Oversampling refers to the grid interval.
2. The Value Grid
Process we usually call quantization which means the value we sample isn't continuous but has discrete property of being a value withing a pre defined set of values (Quantization Grid).
• When you said "So if the modulated signal has a frequency f" do you mean the center frequency of the modulation, or the maximum baseband frequency of the input signal? – Avio Jun 17 '18 at 8:12
• I didn't go into details (As you can actually sample in pass band as well). Let's say $f$ is the highest frequency in the modulated signal (The modulated data). – Royi Jun 17 '18 at 8:26
• Additionally, does the order of modulating and sampling really matter? Can't I first oversample and then modulate instead of what you proposed? – Avio Jun 17 '18 at 8:37
• Oversampling is done on the receiving part of the process. Since the the received signal is already modulated there is no real choice here :-). – Royi Jun 17 '18 at 8:44
• You're welcome. Good Luck! – Royi Jun 17 '18 at 9:43