Given I have an input sequence [ 1 0 1 0 1 0 1 0 ], the DFS is x[n] = 0.5 + 0.5*exp(j*pi*n). The sampling (Ts) is 100 secs. Am I correct in saying that the spectral coefficient 0.5 at pi is equivalent to saying the DFS has a 0.5 peak every 200 secs? My reasoning is between adjacent x[n] samples a time Ts has passed which corresponds to 2*pi of the sampling period. Therefore, half, i.e. pi, is 2 * Ts. Thanks, Aaron
Beginner Question - Discrete Fourier Series and sampling
Started by ●December 12, 2008
Reply by ●December 12, 20082008-12-12
>Given I have an input sequence [ 1 0 1 0 1 0 1 0 ], the DFS is x[n] = >0.5 + 0.5*exp(j*pi*n). The sampling (Ts) is 100 secs. > >Am I correct in saying that the spectral coefficient 0.5 at pi is >equivalent to saying the DFS has a 0.5 peak every 200 secs? > >My reasoning is between adjacent x[n] samples a time Ts has passed >which corresponds to 2*pi of the sampling period. Therefore, half, >i.e. pi, is 2 * Ts. > >Thanks, > >Aaron >In your statement you are confusing some things. First of all the the discrete fourier series refers to the fourier coefficients; saying: "the DFS has a 0.5 peak every 200 secs" is weird. To say that ".. the coefficient 0.5 is equivalent ...", is also a bit confusing. A spectral coefficient of 0.5 at the nyquist frequency indicates that you have a component in your time domain signal which alternates between -0.5/N and 0.5/N with every sample. Maybe that has something to do with what you want to say. I am just saying that it is hard to see whether your _thought_ is correct or not, since alone your formulation is flawed. gr. Bjoern