Use the time-shifting property and the result for the Fourier Transform of a cosine function to calculate the Fourier Transform of a sine function. Show that the phase response at positive and negative frequencies matches the expected result for a sine function.
Use the time-shifting property and the result for the Fourier Transform of a cosine function to...
a) Find the Fourier Transform of the half-cosine pulse shown in Fig. 1(a). b) Then apply the time-shifting property to the result obtained in part a) to evaluate the spectrum of the half-sine pulse shown in Fig. 1(b). c) What is the spectrum of the negative half-sine pulse shown in Fig. 1(e)? d) Find the spectrum of the single sine pulse shown in Fig. 1(d). gft T/2 -T a) Find the Fourier Transform of the half-cosine pulse shown in Fig....
Fourier transform of a rectangular pulse is a: Tan function Cosine function Sinc function Sine function Question 28 1 pts Every periodic function can be expressed as a linear combination of: Sine and cosine functions Sine functions Logarithmic functions None of the above
[b] State and prove frequency shifting property of Fourier transform Also find the fourier transform of gate function. [c] It is given that x[0] =1, x[1]=2, x[2]=1, h[0]=1. Let y[n] be linear convolution of x[n) and h[n]. Given that y[1]=3 and y[2]-4. Find the value of the expression 10y[3]+y[4].
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
Question 27 1 pts Fourier transform of a rectangular pulse is a: Sine function Tan function Sinc function Cosine function D Question 28 1 pts Every periodic function can be expressed as a linear combination of: Sine and cosine functions None of the above Logarithmic functions Sine functions
Use the second shifting property and Table 3.1 to find the Laplace transform of each function. Sketch each function. numbers 27 and 31 please Use the second shifting property and Table 3.1 to find the Laplace transform of each function. Sketch each function. 25. u2(t) 26. u4(t) sin At ro, 0) < t < 2 f(t) = {2t, 2 < t < 4 10, 4<t 28. { – u40) u4(t)6 – t) – u6(t)(6 – t) It, 0 < t...
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...
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's theorem is satisfied for eand its Fourier transform 1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's...
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt).
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt). Please solve clearly, not copy paste old solutions.