ABSTRACT
In Chapter 7 we established that after a signal x(t) is sampled, we can only hope to compute the values of XI (f) = F{x (t) P Δt (t)},which is the Fourier transform of the sampled sequence. As discussed initially in Chapter 6 and more than once in Chapter 7, whether the central period of XI (f) agrees with or closely approximates X(f)= F{x(t)} is determined by the chosen sampling rate ℝ = 1/Δt,which cannot be changed after the signal has been sampled. When they don t agree with each other, the Fourier transform of the sequence XI (f) is said to contain aliased frequencies. While we were concerned with the mathematical relationship between the sample values of XI (f) and the sample values of the signal x(t) in Chapter 7, in this chapter we are concerned with computing the numerical values of XI (f) from a nite sequence of N samples, assuming that we have some knowledge about the duration or periodicity of the signal x(t) so that we can decide on the sample size N.
