Question

Find the signals corresponding to the following spectra. Make use of appropriate Fourier-transform theorems.

X₁(f) = 2cos(2πf) ll(f) exp (-j4πf)

Answer 1

To find the signals corresponding to the given spectra, we need to use the appropriate Fourier-transform theorems. For X₁(f) = 2cos(2πf), the corresponding signal is 2δ(f-f₀) + 2δ(f+f₀). For ll(f) exp (-j4πf), the corresponding signal is δ(f-f₁).

Step-by-step explanation:

In order to find the signals corresponding to the given spectra, we need to use the appropriate Fourier-transform theorems. The given spectra are X₁(f) = 2cos(2πf) and ll(f) exp (-j4πf).

1. For X₁(f), we can apply the theorem that states that the Fourier transform of the cosine function is a combination of two impulses at ±f₀, where f₀ is the frequency of the cosine function. Therefore, the corresponding signal is 2δ(f-f₀) + 2δ(f+f₀).
2. For ll(f), we can apply the theorem that states that the Fourier transform of the complex exponential function e^(-j2πft) is an impulse at the frequency f. Therefore, the corresponding signal is δ(f-f₁), where f₁ is the frequency of the complex exponential function.