Fourier transform and its properties
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1. Compute the Fourier transform for x(t) = texp(-t)u(t)
2. The linearity property of the Fourier transform is defined as:
3. Determine the exponential Fourier series for:
4. Using complex notation, combine the expressions to form a single sinusoid for: cos(10t+ pi/2) + 2cos(10t - pi/3)
5. The polar notation for the function 1 + e^(j4) is:
6. The duality property of the Fourier transform is defined as:
7. A continuous time signal x(t) has the Fourier transform: x(w) = 1/(jwW +b), where b is a constant. Determine the Fourier transform for v(t) = t^2*x(t).
8. Compute the inverse Fourier transform for X(w) = cos(4w).
9. A continuous time signal x(t) has the Fourier transform: x(w) = 1/(jw +b), where b is a constant. Determine the Fourier transform for v(t) = x(t) * x(t).
10. The polar notation for the function 1 + e^(j4) + e^(j2) is:
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Solution Summary
The solution explains the Fourier transform and its properties in detail. It also shows how to represent a function using polar notation.
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