Let as sketched in Figure P2.66, be the impulse responses of three LT1 systems. These t...

Let as sketched in Figure P2.66, be the impulse responses of three LT1 systems. These three signals are known as Walsh functions and are of considerable practical importance because they can be easily generated by digital logic circuitry and because multiplication by each of them can be implemented in a simple fashion by a polarity-reversing switch.

(a) Determine and sketch a choice for x₁ (t), a continuous-time signal with the following properties:

(b) Repeat part each as large as possible at t = 4.

(c) What is the value of

at time t = 4 for i, j = 1, 2, 3?

The system with impulse response in order to produce the maximum output signal. In the next problem, we relate the concept of a matched filter to that of the correlation function for continuous-time signals.