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 $|\omega|<\pi/M$.

If your signal is bandlimited enough, then averaging 10 samples (as a crude lowpass filtering) will suffice. Otherwise, a better filter can be designed by different filter design techniques such as a simple windowed linear phase lowpass filter.

the following matlab excerpt gives you a better result.

K = 15;
h = fir1(2*K, 1/10); % impulse response of a 20th order FIR LPF.
yc = conv(x,h);      % convolve h[n] with x[n] of length L
y = yc(K+1:K+L);     % the filtered signal 
| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.