) as shown in Figure 3.10(b). In words, and it's a mouthful, this bandwidth is the range of frequen- cies from [the frequency, to the right of the peak value of |S(f), at which the first 0 occurs] to [the frequency, to the left of the peak value of |S(f), at which the first 0 occurs]. So, for example, for the |S(f)| of Figure 3.9 redrawn in Figure 3.10(b), the first zero to the right of the peak is at f=fc- -1/T, and the first zero to the left of the peak is at f = fc + 1/T, SO the null-to-null bandwidth is 2/T. 3-dB bandwidth: the range of frequencies in S(f) (or |S(f)|) as shown in Figure 3.10(c). In words and, again, it's a mouthful: the range of frequencies from [the fre- quency to the right of the peak value of S(f) where |S(f) is half its peak value] to [the frequency on the left of the peak where |S(f)| is half its peak value]. Now you know how to figure out the bandwidth of a signal. Typically, when I use the word bandwidth, often written BW for short, I'll be referring to the null-to-null bandwidth. 3.3.4 A Linear Time Invariant (LTI) System Figure 3.11 shows a system with an input x(t) and an output y(t). You'll notice the system is called LTI, which means (1) it's linear. if I put in ax, (t)+bx,(t), I'll get out ay (t)+by2(t). Here, (t) is the system's response to X1 (t), and ly(t) is the system's response to x 2 (t); (2) it's time invariant: if I put in x(t-T), I'll get out y(t-T)-that is, a delay in the input creates a delay in the output. There is just one thing I want you to know about an LTI system. Let's say you find out that the system output is y(t) = h(t) when the system input is the impulse x(t) = S(t). Just by knowing this one little thing, h(t), called the impulse response, you can get the output y(t) for any input x(t). All you have to do to get the output, given the input x(t), is calculate an integral called convolution. It goes like this: Linear Time Invariant (LTI) Input Output System Figure 3.11 LTI system Chapter Three (3.15) Sometimes calculating this integral can be a pain. In that