Question

x[n] 0.2 + z?¹ 0.4 + 0.4 z?¹ z?¹ 0.2 + 0.2 y[n] FIGURE 1.8 Example block diagram. 5. a. Write the difference equation corresponding to the block diagram in Figure 1.8. Is this an FIR or IIR filter? Why? b. From the difference equation, take the Z transform and derive the transfer function $H(z) = Y(z)/X(z)$. c. What are the values of $H(z)$ at $z = e^{j\theta} = 1$ and $e^{j\pi} = -1$? Roughly, how does this filter affect the frequency content of the input signal?

          x[n]
0.2
+
z?¹
0.4
+
0.4
z?¹
z?¹
0.2
+
0.2
y[n]
FIGURE 1.8
Example block diagram.
5. a. Write the difference equation corresponding to the block diagram in Figure 1.8. Is this an FIR or IIR filter? Why?
b. From the difference equation, take the Z transform and derive the transfer function $H(z) = Y(z)/X(z)$.
c. What are the values of $H(z)$ at $z = e^{j\theta} = 1$ and $e^{j\pi} = -1$? Roughly, how does this filter affect the frequency content of the input signal?

x[n]
0.2
+
z?¹
0.4
+
0.4
z?¹
z?¹
0.2
+
0.2
y[n]
FIGURE 1.8
Example block diagram.
5. a. Write the difference equation corresponding to the block diagram in Figure 1.8. Is this an FIR or IIR filter? Why?
b. From the difference equation, take the Z transform and derive the transfer function H(z) = Y(z)/X(z).
c. What are the values of H(z) at z = e^jθ = 1 and e^jπ = -1? Roughly, how does this filter affect the frequency content of the input signal?

Added by Mar-A H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Stephen Zaffke

Step 1

The output y[n] is the sum of the current and past weighted inputs and outputs. The difference equation can be written by tracing the signal flow from x[n] to y[n]: y[n] = 0.2x[n] + 0.4x[n-1] + 0.2x[n-2] - 0.4y[n-1] - 0.2y[n-2] Show more…

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a) Write the difference equation corresponding to the block diagram in this figure. Is this an FIR or IIR filter? Why? b) From the difference equation, take the Z transform and derive the transfer function H(z) = Y(z)/X(z) c) What are the values of H(z) at z = e^j0 = 1 and e^j(pi) = -1? Roughly, how does this filter affect the frequency content of the input signal? x[n] y[n] FIGURE 1.8 Example block diagram 5. a. Write the difference equation corresponding to the block diagram in Figure 1.8. Is this an FIR or IIR filter? Why? b. From the difference equation, take the Z transform and derive the transfer function H(z) = Y(z)/X(z). c. What are the values of H(z) at z = e^j0 = 1 and e^j(pi) = -1? Roughly, how does this filter affect the frequency content of the input signal?