t Find the Fourier transform of (t) that is equal to -1 fort between-2 and zero,...
5. Consider the 'top-hat' function which is zero everywhere except between -1 and 1 where it takes value 1. Show, using only elementary integration, that the convolution of this function with itself gives a 'triangular function', 0 0 x〉2 which you should sketch Find the Fourier transform of the 'triangular function' f(x) using the result for the Fourier transform of a convolution.
5. Consider the 'top-hat' function which is zero everywhere except between -1 and 1 where it takes value...
Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of the Fourier transform found in the "Properties of Fourier Transforms" table in textbook and the "Famous Fourier Transforms Table" in textbook instead of direct integration as much as possible to simplify your calculation wherever appropriate: 2-2
Use tables of Fourier transform pairs and properties to find the
Fourier transform of each of the signals
a) f(t)=(1-eb )u(t) b) f(t)= Acos(@t+) c) f(t)=e"u(-t), a>0 d) f(t)=C/(t+t)
2. Consider the Fourier Transform pair: e11 - 1+ 2 Use the Fourier transform properties to find the Fourier transform of: x(t) = te
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
Find the Fourier Transform of the triangular pulse _(1 + t for -1<t < 0 x(t) = (1 - t for 0 <t<1
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of the following signals Hint: use the properties of Fourier transform) a. v(t)-x(1):cos(10π t) d. v(t)X(t) e. v()-e"x(t-1)
2 part a and b , 3 part a and b
7 marks 2. Consider the Fourier transform pair a) Use the appropriate Fourier transform properties to find the Fourier transform of te-lti 5 marks) b) Use the results from part (a) and the duality property to determine the Fourier transform of 4t f(t) = (1 +t2)2 [15 marks 3. For the discrete time system shown in fig. 1 a) Determine the transfer function Hint: The best starting point is...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
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...