is obtained, approximately, by summing the rectangular areas. The result so obtained is the convolution of a rectangular pulse with step size W with the impulses located at the sampling instants with weights equal to the sample values. In consequence, the spectrum of interest will have superimposed upon it the frequency response of the sample and hold, and the spectrum of the sampled singnal Ss is given by: The first part of the expression, i.e. the 'sin(x)/x' part, is the frequency response of the sample and hold. Its amplitude decreases with frequency and it falls to 63% of its peak value at half the sampling frequency and it is zero at multiples of that frequency (since fs =1/W). The second term in the equation is called the Fourier transform of the discrete signal sn. It is a continuous function over all and involves an infinite number of summations. In practice the summation process can be truncated to a finite number of samples, N, possibly because the waveform is periodic or zero outside the range of samples. Furthermore, because the same spectrum is endlessly repeated, it is possible to confine interest to spectral data within the range -/2 to +/2. As an example, an exponential chirp (with its top frequency well below the Nyquist limit) is sampled at 256 points, as shown. The sampled spectrum, Ss() of this waveform, calculated using the equation given above, is shown. To simplify the plot, only the results at positive frequencies have been displayed. The influence of the frequency spectrum of the zero order hold circuit is clearly seen in the diagram. The baseband portion of the spectrum is shown in more detail in the next figure and the response shows a distinct slope, being significantly lower at the higher frequencies. Although the characteristic of the zero order hold has a small influence on this result, the slope is mainly due to the properties of the chirp. The waveform sweeps relatively quickly over the high frequencies and spends more time sweeping the low frequencies, consequently there is less energy content at the high frequencies with more at the lower ones. (A linear chirp, on the other hand, has a nominally flat spectrum because its frequencies are swept at the same rate, as shown in some earlier plots). Via the discrete Fourier transform If we limit interest in the output spectrum to a finite number of