Histogram of Sinusoid: Is it the Same as PDF?

[X1088LoD]

I am looking at values of a sinusoid, y = A sin(2*Pi*f*t), oscillating between A and -A at a frequency of 25 Hz over 0.650 milliseconds.

If I find the histogram of the sinusoid, is this the same thing as the probability density function of that sinusoid? If this is not the case, what does the histogram represent in terms of statistical analysis?

I appreciate it.

~ Brent Ellis

 

[mathman]

The histogram is a representation of the probability density function. If you get it by some experimental menas, it is an approximation. If you get it from theory, then it will be exact if you don't average over intervals (sorting into bins is what a histogram usually refers to).

 

[X1088LoD]

so let's say I got my data by means of measurements, 4096 data points total, then i sort them into histogram form

If each bin is represented by 1 value, If I divide each point by 4096, would that normalize the plot into the actual (approximation) PDF?

 

[Krusty]

If the data you have collected is continuous, which i think is the case, then you can't let one bin represent one value, it has to be a range of values. The smaller the range of values, or the larger the number of bins you use, the closer you will get to approximating the true underlying pdf. Of course, the histogram has to be standardized so that the y-axis represents a proportion of observations per bin, so divide the frequencies of each bin by 4096.