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The TFS for an arbitrary signal, x(t), where To=1 ms, is given by ((300n)×(-1)") *(-¹²) si x(t): = 10+ n=1 400 3n-5 cos (nat)+) n=1 n² +1 sin (not) Furthermore, it is passed through an ideal filter, wherein magnitude and phase are neither amplified nor attenuated up to and including 2kHz, whereas all other harmonics are annihilated. F=2KH ===> -36.96 Sketch the spectrum of the output signal's EFS, both magnitude (dB, with significant digit of 1 dB) and phase (degrees, with significant digit of 1 degree) including DC. Recall, dB = 20log10 (magnitude). Label, and place numerical values on your axes and elsewhere, not just a quick sketch! | Prld B 20 1 ALPn (0°) 2 nwo nwo

The TFS for an arbitrary signal, x(t), where To=1 ms, is given by ((300n)×(-1)") *(-¹²) si x(t): = 10+ n=1 400 3n-5 cos (nat)+) n=1 n² +1 sin (not) Furthermore, it is passed through an ideal filter, wherein magnitude and phase are neither amplified nor attenuated up to and including 2kHz, whereas all other harmonics are annihilated. F=2KH ===> -36.96 Sketch the spectrum of the output signal's EFS, both magnitude (dB, with significant digit of 1 dB) and phase (degrees, with significant digit of 1 degree) including DC. Recall, dB = 20log10 (magnitude). Label, and place numerical values on your axes and elsewhere, not just a quick sketch! | Prld B 20 1 ALPn (0°) 2 nwo nwo

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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The TFS for an arbitrary signal, \( x(t) \), where \( T_0 = 1 \, \text{ms} \), is given by: \[ x(t) = 10 + \sum_{n=1}^{\infty} \left(\frac{400}{3n-5}\right) \cos(n \omega_0 t) + \sum_{n=1}^{\infty} \left(\frac{(300n)(-1)^n}{n^2+1}\right) \sin(n \omega_0 t) \] Furthermore, it is passed through an ideal filter, wherein magnitude and phase are neither amplified nor attenuated up to and including \( 2 \, \text{kHz} \), whereas all other harmonics are annihilated. Sketch the spectrum of the output signal’s EFS, both magnitude (dB, with significant digit of 1 dB) and phase (degrees, with significant digit of 1 degree) including DC. Recall, dB = \( 20 \log_{10} (\text{magnitude}) \). **Graph Description:** 1. **Magnitude Graph (Top):** - The y-axis represents the magnitude in decibels (dB). - The x-axis is labeled as \( n \omega_0 \), where \( n \) represents harmonic frequencies. - The plot shows a magnitude of approximately 20 dB at the DC component (n=0). - The magnitude at \( n=1 \) is marked as approximately -36.96 dB. - Beyond this, there are no other significant elements on the graph, indicating anhiliation of harmonics beyond 2 kHz. 2. **Phase Graph (Bottom):** - The y-axis represents the phase angle \( \angle D_n (\theta^\circ) \) in degrees. - The x-axis is again labeled as \( n \omega_0 \). - The phase diagram appears to show no significant phase deviation, indicating the ideal filter’s characteristic of maintaining phase angles unchanged for frequencies under 2 kHz. **Instructions:** Label and place numerical values on your axes and elsewhere, ensuring it is more than just a quick sketch!
Transcribed Image Text:The TFS for an arbitrary signal, \( x(t) \), where \( T_0 = 1 \, \text{ms} \), is given by: \[ x(t) = 10 + \sum_{n=1}^{\infty} \left(\frac{400}{3n-5}\right) \cos(n \omega_0 t) + \sum_{n=1}^{\infty} \left(\frac{(300n)(-1)^n}{n^2+1}\right) \sin(n \omega_0 t) \] Furthermore, it is passed through an ideal filter, wherein magnitude and phase are neither amplified nor attenuated up to and including \( 2 \, \text{kHz} \), whereas all other harmonics are annihilated. Sketch the spectrum of the output signal’s EFS, both magnitude (dB, with significant digit of 1 dB) and phase (degrees, with significant digit of 1 degree) including DC. Recall, dB = \( 20 \log_{10} (\text{magnitude}) \). **Graph Description:** 1. **Magnitude Graph (Top):** - The y-axis represents the magnitude in decibels (dB). - The x-axis is labeled as \( n \omega_0 \), where \( n \) represents harmonic frequencies. - The plot shows a magnitude of approximately 20 dB at the DC component (n=0). - The magnitude at \( n=1 \) is marked as approximately -36.96 dB. - Beyond this, there are no other significant elements on the graph, indicating anhiliation of harmonics beyond 2 kHz. 2. **Phase Graph (Bottom):** - The y-axis represents the phase angle \( \angle D_n (\theta^\circ) \) in degrees. - The x-axis is again labeled as \( n \omega_0 \). - The phase diagram appears to show no significant phase deviation, indicating the ideal filter’s characteristic of maintaining phase angles unchanged for frequencies under 2 kHz. **Instructions:** Label and place numerical values on your axes and elsewhere, ensuring it is more than just a quick sketch!
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