Basic Sampling Question: Understanding Frequency Change in Piecewise Sinusoid

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In summary, a continuous sinusoid given by #f(t) can be sampled at a sampling rate of f_s = 4f_0, where f_s is the sampling frequency and f_0 is the frequency of the sinusoid. This may lead to confusion as the coefficient inside the sinusoid changes due to the independent variable being n instead of time. To better understand this, try finding the relationship between n and f_0 and see how it affects the sinusoid.
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CoolDude420
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Homework Statement


Hi, I have the following continuous sinusoid given by

6ca168c1f4.png


Now, if I sample this with a sampling rate of $$f_s = 4f_0$$

, I am told this is the answer,

7d422e4e0e.png


I don't understand that. How come the frequency of the sinusoid has changed? I already studied sampling, etc. but this is the first time I've come across it in a piecewise manner like this. I can't seem to understand what just happened?

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The Attempt at a Solution

 

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  • #2
The frequency hasn't changed. The coefficient inside has changed because your independent variable is no longer time, but ##n##. Try coming up with ##n## as a function of ##f_0## and ##t## and see what you get.
 

What is basic sampling?

Basic sampling is a method used in research to collect data from a smaller group of individuals that represents a larger population. It involves selecting a random sample from the population in order to make inferences about the whole population.

Why is basic sampling important?

Basic sampling is important because it allows researchers to draw conclusions about a larger population without having to collect data from every single individual. This makes the research process more efficient and cost-effective.

What are the different types of basic sampling?

The main types of basic sampling are simple random sampling, systematic sampling, stratified sampling, and cluster sampling. Each method has its own advantages and is used depending on the research objectives and the characteristics of the population.

What is the difference between a sample and a population?

A sample is a subset of a population, while a population refers to the entire group of individuals that the researcher is interested in. Samples are used to make inferences about the larger population.

What are the potential sources of bias in basic sampling?

Potential sources of bias in basic sampling include non-response bias, where certain individuals in the population are less likely to participate in the study, and selection bias, where the sample is not representative of the population due to the sampling method used. It is important for researchers to be aware of these potential biases and take steps to minimize them.

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