### Problem 4: Frequency Response of a Stable Linear FilterThe frequency response of a stable Linear Filter is depicted below, with the magnitude given in decibels (dBs) and the phase in degrees.#### Frequency Response Graphs1. **Magnitude Plot (Top Graph)** - **Vertical Axis (Magnitude in dB)**: This shows the level of the frequency response in decibels. Values range from -80 dB to 0 dB. - **Horizontal Axis (Normalized Frequency)**: This is normalized to \(\pi\) radians per sample (rad/sample), ranging from 0 to 1. The graph exhibits periodic nulls (zero magnitude points) at regular intervals in the normalized frequency domain.2. **Phase Plot (Bottom Graph)** - **Vertical Axis (Phase in degrees)**: This shows the phase shift introduced by the filter in degrees, with values ranging from -200 to 100 degrees. - **Horizontal Axis (Normalized Frequency)**: As with the magnitude plot, this is also normalized to \(\pi\) radians per sample (rad/sample), ranging from 0 to 1. The phase response is a linear descending pattern, resetting every 0.2 units in the normalized frequency axis.#### Problem StatementDetermine the best approximation of the output signal \( y[n] \) when the input signal is given by:\[ x[n] = 3 + 2 \cos (0.1 \pi n + 0.1\pi) + 2 \cos (0.5 \pi n) \]#### Important NoteRecall that a value \( X_{dB} \) is related to \( X \) by the following equation:\[ X_{dB} = 20 \log_{10} (X) \]and therefore, \[ X = 10^{X_{dB}/20} \]---To solve the problem, analyze the input signal's frequency components and correlate them with the filter's response characteristics. Use the provided frequency responses to determine how each component of the input signal is affected by the filter.

Linear time invariant system : Output of a linear time invariant system with impulse response x[n]…

-20 40 -60 -80 0.4 0.2 Normalized Frequency (x rad/sample) 0.1 0.3 0.5 0.6 0.7 0.8 0.9 1. 100 -100 -200 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 Normalized Frequency (xa rad/sample) Determine, to your best approximation, the output signal y[n] when the input signal is x[n] = 3+2cos(0.1zn+0.17)+2cos(0.5an) Phase (degrees) Magnitude (dB)

-20 40 -60 -80 0.4 0.2 Normalized Frequency (x rad/sample) 0.1 0.3 0.5 0.6 0.7 0.8 0.9 1. 100 -100 -200 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 Normalized Frequency (xa rad/sample) Determine, to your best approximation, the output signal y[n] when the input signal is x[n] = 3+2cos(0.1zn+0.17)+2cos(0.5an) Phase (degrees) Magnitude (dB)

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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