1. Consider an FIR filter whose impulse response is that shown in Figure P5–10(a). Given the x ( n )

1. Consider an FIR filter whose impulse response is that shown in Figure P5–10(a). Given the x ( n ) filter input sequence shown in Figure P5–10(b), draw the filter’s output sequence. 2. Regarding the material in this chapter, it’s educational to revisit the idea of periodic sampling that was presented in Chapter 2. Think about a continuous x ( t ) signal in Figure P5–11(a) whose spectrum is depicted in Figure P5–11(b). Also, consider the continuous periodic infinitely narrow impulses, s ( t ), shown in Figure P5–11(c). Reference [28] provides the algebraic acrobatics to show that the spectrum of s ( t ) is the continuous infinitely narrow impulses, S ( f ), shown in Figure P5–11(d). If we multiply the x ( t ) signal by the s ( t ) impulses, we obtain the continuous y ( t ) = s ( t ) x ( t ) impulse signal shown by the arrows in Figure P5–11(e). Now, if we use an analog-to-digital converter to represent those y ( t ) impulse values as a sequence of discrete samples, we obtain the y ( n ) sequence shown in Figure P5–11(f). Here is the problem: Briefly discuss what we learned in this Chapter 5 that tells us the spectrum of the y ( n ) samples comprises periodic replications of the X ( f ) in Figure P5–11(b). Your brief discussion should confirm the material in Chapter 2 which stated that discrete-time sequences have periodic (replicated) spectra.