# How good or bad my downsampled data is?

Suppose I have time series data at a one-minute resolution. Now I downsample data by taking mean of every 10-minute window, i.e., after downsampling, 60 readings will reduce to 6 readings. How should I show how good or bad my downsampling technique is? In a good downsampling technique, the downsampled sample should closely represent the original data.

First look at the spectrum of the original data $$x[n]$$. Downsampling a discrete-time signal $$x[n]$$ by $$M=10$$ requires that (to prevent aliasing) the signal should be bandlimited to $$|\omega|<\pi/M$$.
K = 15;