1. A 5-point moving averager can be described by the following equation:
The averager's signal-flow block diagram is shown in the diagram below, where x(n) input samples flow through the averager from left to right.
(a) Draw the impulse response of the averager. !
(b) Draw the block diagram of the discrete system described by the equation below:
(c) Is the averager defined in (b) identical to the original one? If so, if you need to
implement the averager programmatically, would you prefer the original averager or you would like to implement the one defined in (b)? Explain why. !
2. An A/D converter that is capable of sampling an analog signal at a sample rate of 100 MHz. The A/D converter has internal memory that can store up to 4x106 discrete samples. What is the maximum number of cycles of a 25 MHz analog sine wave that can be stored in the A/D converter's memory? Show clearly all the calculations involved. !!
3. Consider the two continuous signals defined by
a(t) = cos(4000πt) and b(t) = cos(200πt)
whose product yields the x(t) signal shown in the figure below
What is the minimum sample rate fs, measured in Hz, that would result in a sequence
x(n) with no aliasing errors (i.e. no spectral replication overlap)?