Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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!](https://content.bartleby.com/qna-images/question/77ad9bfd-a431-4f88-9f4e-7c7ecff8f29b/307a8d92-a024-4252-8100-0d6c11397b77/080twj_processed.jpeg)
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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