Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H...
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...
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier series: i) 2 Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2
Fourier Integral #3 is demostrate Fourier Integral and #4 is calculate transform Integral de Fourier 4w B(w) = T(1 + w?)? 3. Sea: f(x) = xe-HI Pruebe que: A(w) = 0 Transformada 4. Calcule la transformada de f(x) = || if 0 5x<1 0 otherwise ---
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)
8. (a) Find the Fourier transform of the signal by direct integration. f(t) = ((t-5)+e-Y(-5))u(t-5) (5 points) (b) Use the convolution theorem of Fourier transform, find the convolution of the following signals: (5 points) x(t) = 5e-4tu(t) and h(t) = 7e-3tu(t)
1. Find the Fourier transforms of the following functions: (1) f(x) = rect * (x) * r * e * c * t * (x - 1) (2) g(x) = 2sin c * (2x) * sin(x) (3) p(x) = rect(x - 2)/2x (4) u(x) = 3sin c * (3x) - sin c * (x) (5) v(x) = sinc(x) * sinc (x) * sinc (x) 2. Find and sketch the functions and the corresponding Fourier transforms: (1) f(x) = 1/5 *...
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)-...
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)...
2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3 2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3