# Redundancy when using Nyquist rate for a time series

I sample temperature at one sample per second (the hardware I am using takes the temperature at this rate, so this is the max I can efficiently sample.) The Nyquist rate for this signal would be 2 samples / second, correct? If so, both samples (for any given second) will be the same, and so redundant. For discrete time series does the Nyquist rate apply? I am sure my logic is wrong somewhere, but what am I missing?

• There's at least two questions here, and both are vague. If you sample the temperature at one sample per second, you're done -- you have a 1Hz sample rate. Why do you then want to sample again? What do you hope to gain, or lose? Aug 4 '20 at 21:08
• For discrete time series does the Nyquist rate apply? Yes, in the sense that if you undersample the series, then there are constraints on the maximum bandwidth you can encode (or, in reverse, if you want to undersample at some rate, you need to limit the bandwidth to avoid aliasing). Also in the sense that if -- to choose a not-random example -- you upsample from 1Hz to 2Hz, only the signal content from -1/2Hz to +1/2Hz is unique; the rest is redundant. Aug 4 '20 at 21:11