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Consider the real, frequency-domain function illustrated in the given figure. -f If A = 3, 4 = 95 kHz, and 2 = 105 kHz, the Inverse CTFT of the given function is z (t) Xsinc (Yt) cos (Z x 10°nt) The numerical values of the constants are X=| 50000 10000. and Z=

Consider the real, frequency-domain function illustrated in the given figure. -f If A = 3, 4 = 95 kHz, and 2 = 105 kHz, the Inverse CTFT of the given function is z (t) Xsinc (Yt) cos (Z x 10°nt) The numerical values of the constants are X=| 50000 10000. and Z=

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Frequency-Domain Function Analysis Consider the real, frequency-domain function illustrated in the given figure: --- #### Diagram Explanation - **Graph Description:** - The horizontal axis represents frequency \( f \). - The vertical axis represents the magnitude of the function \( |X(f)| \). - The function is non-zero and constant over three frequency bands, forming a symmetrical shape resembling two continuous rectangles centered at the origin and extending both positively and negatively along the frequency axis. - The frequency bands are centered at \( f_1 = 95 \) kHz and \( f_2 = 105 \) kHz, with corresponding negative frequencies \( -f_1 \) and \( -f_2 \). --- #### Inverse Continuous-Time Fourier Transform Given: - \( A = 3 \) - \( f_1 = 95 \) kHz - \( f_2 = 105 \) kHz The inverse Continuous-Time Fourier Transform (CTFT) of the given function is: \[ x(t) = X \text{sinc}(Yt) \cos(Z \times 10^5 \pi t) \] #### Numerical Values of Constants - \( X = 50000 \) - \( Y = 10000 \) - \( Z = 2 \) --- This description provides a detailed understanding of the frequency-domain function and how to derive its time-domain representation using inverse CTFT.
Transcribed Image Text:### Frequency-Domain Function Analysis Consider the real, frequency-domain function illustrated in the given figure: --- #### Diagram Explanation - **Graph Description:** - The horizontal axis represents frequency \( f \). - The vertical axis represents the magnitude of the function \( |X(f)| \). - The function is non-zero and constant over three frequency bands, forming a symmetrical shape resembling two continuous rectangles centered at the origin and extending both positively and negatively along the frequency axis. - The frequency bands are centered at \( f_1 = 95 \) kHz and \( f_2 = 105 \) kHz, with corresponding negative frequencies \( -f_1 \) and \( -f_2 \). --- #### Inverse Continuous-Time Fourier Transform Given: - \( A = 3 \) - \( f_1 = 95 \) kHz - \( f_2 = 105 \) kHz The inverse Continuous-Time Fourier Transform (CTFT) of the given function is: \[ x(t) = X \text{sinc}(Yt) \cos(Z \times 10^5 \pi t) \] #### Numerical Values of Constants - \( X = 50000 \) - \( Y = 10000 \) - \( Z = 2 \) --- This description provides a detailed understanding of the frequency-domain function and how to derive its time-domain representation using inverse CTFT.
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