1. The value of the integral is equal to
2. Suppose the maximum frequency in a band limited signal x(t) is 5 kHz. Then, the maximum frequency in x(t) cos(2000πt), in kHz is
3. Consider a signal defined by
Its Fourier transform is
4. A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier transforms are X(ω) and Y(ω). Which of the following statements is true?
- X(ω) and Y(ω) are both real
- X(ω) is real and Y(ω) is imaginary
- X(ω) and Y(ω) are both imaginary
- X(ω) is imaginary and Y(ω) is real
5. The Fourier transform of a signal h(t) is H(jω) = (2cosω)(sin2ω)/ω. The value of h(0) is
6. A signal is represented by
The Fourier transform of the convolved signal
y(t) = x(2t) ∗ x(t/2) is
7. Let f(t) be a continous time signal and let F(ω) be its Fourier transform defined by
and g(t) is defined by
What is the relationship between f(t) and g(t)?
- g(t) would always be proportional to f(t).
- g(t) would be proportional to f(t) if f(t) is an even function
- g(t) would be proportional to f(t) only if f(t) is a sinusoidal function.
- g(t) would never be proportional to f(t)
8. Let , x(t) = rect(t-1/2) (where, rect(t) = 1 for -1/2 ≤ x ≤ 1/2 and zero otherwise). Then sinc(x) = sin(πx)/πx, the Fourier transform of x(t) + x(-t) will be given by