Frequency range and resolution

As mentioned before, the smallest observable frequency (v ,in) in a continuous signal is the reciprocal of the measurement time ( I2T ). Because only those frequencies are considered which exactly fit in the measurement time, all frequencies should be a multiple of namely n/2T with n = - to -l-oo. As a result the Fourier transform of a continuous signal is discrete in the frequency domain, 

In summary, the Fourier transform of a continuous signal digitized in 2A/ + 1 data points returns N real Fourier coefficients, N imaginary Fourier coefficients and the average signal, also called the DC term, i.e. in total 2N + 1 points. The relationship between the scales in both domains is shown in Fig. 40.9. 

Signal measured at five time points with At = 0.5 s and 27 = 2 s 

Original time scale (seconds) Time scale with origin shifted to the centre k  

By way of illustration we calculate the FT of the discrete signal listed in Table 40.1. The origin of the time domain has been placed in the centre of the data. 

---