Answer Happy

Figure P.3.3-2 3.3-2 The Fourier transform of the triangular pulse g(t) in Fig. P3.3-2a is given as G(f)= (2x)² (2x-j2f³2f-1) Use this information, and the time-shifting and time-scaling properties, to find the Fourier transforms of the signals shown in Fig. P3.3-2b-f. Hint: Time inversion in g(r) results in the pulse 81 (t) in Fig. P3.3-2b; consequently g₁ (t) = 8(-1). The pulse in Fig. P3.3-2c can be expressed as g (1-7)+81 (1-7) [the sum of g (t) and g₁ (1) both delayed by TJ. Both pulses in Fig. P3.3-2d and e can be expressed as g(t-T) +81(t+T) [the sum of g (1) delayed by T and g₁ (1) advanced by T] for some suitable choice of T. The pulse in Fig. P3.3-2f can be obtained by time-expanding g (r) by a factor of 2 and then delaying the resulting pulse by 2 seconds [or by first delaying g (r) by 1 second and then time-expanding by a factor of 2]. g(r) 8,(1) NAM (b) (a) Problems 133 1.5 8₂ (t) 8(t) AR 0 0 8₂(1)