Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![**Problem BC:5.3**
In the flow diagram shown in Figure 3, the blocks with the "D" represent a one-step time delay. Find the difference equation in the form:
\[
\sum_{k=0}^{N} a_k y[n-k] = \sum_{p=0}^{M} b_p x[n-p]
\]
where \( a_0 = 1 \).
**Flow Diagram Explanation:**
The diagram consists of interconnected blocks and summing junctions as follows:
1. **Inputs and Outputs:**
- Input: \( x[n] \)
- Output: \( y[n] \)
2. **Blocks and Operations:**
- The input \( x[n] \) is multiplied by 40, leading to the first summing junction.
- The initial summation forms a signal \( q[n] \) which passes through a delay block labeled "D".
- This delayed signal is then multiplied by \(-0.9\) and fed back into the first summing junction, completing the feedback loop for \( q[n] \).
- Separately, another path multiplies \( x[n] \) by \(-25\), leading to a second summing junction, forming signal \( w[n] \).
- This \( w[n] \) also passes through a delay block "D".
- The delayed \( w[n] \) signal is multiplied by 0.2 and added as feedback into the second summing junction.
- Both processed paths, \( q[n] \) and \( w[n] \), combine at the final summing junction resulting in the output \( y[n] \).
**Figure Caption:**
Figure 3: Flow diagram for Problem BC: 5.3
This diagram visually represents a linear, time-invariant digital filter system, focusing on how different components influence the system's response to the input signal.](https://content.bartleby.com/qna-images/question/028a22e8-f094-478d-95cf-e0334af4f4a7/f3927730-a09e-43a3-90ef-eba344ef22ad/ywbzbzb_processed.jpeg)
Transcribed Image Text:**Problem BC:5.3**
In the flow diagram shown in Figure 3, the blocks with the "D" represent a one-step time delay. Find the difference equation in the form:
\[
\sum_{k=0}^{N} a_k y[n-k] = \sum_{p=0}^{M} b_p x[n-p]
\]
where \( a_0 = 1 \).
**Flow Diagram Explanation:**
The diagram consists of interconnected blocks and summing junctions as follows:
1. **Inputs and Outputs:**
- Input: \( x[n] \)
- Output: \( y[n] \)
2. **Blocks and Operations:**
- The input \( x[n] \) is multiplied by 40, leading to the first summing junction.
- The initial summation forms a signal \( q[n] \) which passes through a delay block labeled "D".
- This delayed signal is then multiplied by \(-0.9\) and fed back into the first summing junction, completing the feedback loop for \( q[n] \).
- Separately, another path multiplies \( x[n] \) by \(-25\), leading to a second summing junction, forming signal \( w[n] \).
- This \( w[n] \) also passes through a delay block "D".
- The delayed \( w[n] \) signal is multiplied by 0.2 and added as feedback into the second summing junction.
- Both processed paths, \( q[n] \) and \( w[n] \), combine at the final summing junction resulting in the output \( y[n] \).
**Figure Caption:**
Figure 3: Flow diagram for Problem BC: 5.3
This diagram visually represents a linear, time-invariant digital filter system, focusing on how different components influence the system's response to the input signal.
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