4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0, otherwise 2(t-1 Find the output response y(t) when the input is (t)-sinc 2 (a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier...
3. (a) Let () be the rectangular pulse Il-oa()e-a, a 0 otherwise. Show that la sinc ka where sincx(note: in Engineering the alternate definition sincis often used). Use the symmetry of Fourier transform process to deduce that the Fourier transform of sinc i:s (b) Show that the' n-translates of sincTI are orthonormal 1 m n sinc π(x-m) sinc π(1-n) dr= 16 m メn. Hint: Use the shifting and scaling properties together with the Plancherel formula. 3. (a) Let () be...
4) The Fourier transform of the triangular pulse x(t) in Fig. P7.3-4 is expressed as Use this information, and the time-shifting and time-scaling properties, to find the Fourier transforms of the signal shown below ts(t) -1.5-0.50.51.5
4. (I+1+1* pt) Consider a cosine pulse 0, otherwise. 0.8 The magnitude of its Fourier transform is plotted in Figure 2. Find the following parameters of the pulse from the plot: 0.6 C. A= 4 Note that they are all integers. Figure 2
(Using the modulation property) (a) Determine the Fourier transform of the sequence 0, otherwise. (b) Consider the sequence win-ı弡ーcos(쮜. 2π n 0 otherwise. Sketch win] and express We), the Fourier transform of win], in terms of R (el, the Fourier transform of In]. (Hint First express win] in terms of In] and the complex exponentials el (2M) and el 2n/M)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution) 3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
Please finish these questions. Thank you Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...
Write the time domain function r(t) of the graph below as the sum of two rectangular pulse functions, then compute the fourier transform X(w) in terms of sinc function. (Reminder: A rectangular pulse centered 50,427 at the origin with width 27 is defined as II(t) = 11, -T<t<+T and it has the fourier transform II(t) sincwr)) 1 0 Amplitude -1 -2 0 2 3 8 9 10 11 5 6 7 Time-
Find the Fourier Transform of the triangular pulse _(1 + t for -1<t < 0 x(t) = (1 - t for 0 <t<1