EE341
1. (6 pts) Consider a causal LTI system described by the following difference equation:
y(n) = —0.8y(n — 1) + x(n)
a) Is this system a FIR or IIR filter? Explain.
b) Find the frequency response H(Q) of the system. Plot |H(Q)|. Prove that |H(Q)|
is symmetric.
c) Is this system a low-pass or high-pass filter? Explain.
d) Consider the following signal:
x(n) = 5 + 10sin(an/6) + 10cos(an/2), -oo<n<too
Is this signal periodic? What is its period? Plot |X(0)|, where X(Q) is the DTFT
of x(n).
e) Determine the response y(n) of the system to the input signal x(n) in question d).
f) Plot |¥(Q)|, where Y(Q) is the DTFT of y(n). Comment.
g) Consider x(n) = x(n), n=0,1,..,11. Find the 12-point DFT Xo(k) of x(n).Plot
IXo(K)I-
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a s...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a sin(na) π (na) where (Q is the cut-off frequency [-consoo] ii Is hIn] a FIR or an IIR filter? Is it causal or anti-causal filter? Explain 3 your answer. iii) If g. 0.1 π, plot the magnitude responses for the following impulse responses:
The transfer function of an ideal low-pass filter is given by: 4. a) i...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the imp...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
a) The transfer function of an ideal low-pass filter is and its impulse response is where...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the outp...
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Pr...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a sin(na) π (na) where (Q is the cut-off frequency [-consoo] ii Is hIn] a FIR or an IIR filter? Is it causal or anti-causal filter? Explain 3 your answer. iii) If g. 0.1 π, plot the magnitude responses for the following impulse responses:
The transfer function of an ideal low-pass filter is given by: 4. a) i...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Most questions answered within 3 hours.
-
How is an organization's culture learned? How are the
mores and folkways of the organization passed...
asked 7 minutes ago -
If someone could solve this and explain how they did so that
would be great.
I...
asked 8 minutes ago -
What would be the formal charge on the nitrogen atom in a
compound that had a...
asked 8 minutes ago -
Please, i need Unique answer, Use your own words (don't copy and
paste). *Please, don't use...
asked 9 minutes ago -
Two wave pulses travel on a string toward each other. The wave
pulses can be described...
asked 26 minutes ago -
1.A solution has a pH of 5.5. What would be the color of the
solution if...
asked 39 minutes ago -
Over time, hydrogen peroxide, H2O2,
degrades into water and oxygen gas. A bottle of hydrogen
peroxide is...
asked 33 minutes ago -
2. Consider the following data table for a hypothetical
economy.
Aggregate
Consumption
Personal
&n
asked 38 minutes ago -
Adidas Runs Into Supply-Chain Problems in Crucial North
American Market
Shares fall amid concern the sporting-goods...
asked 39 minutes ago -
The physical plant at the main campus of a large state
university recieves daily requests to...
asked 1 hour ago -
Determine the probability p(2) for a binomial
experiment with n=12 trials and the success probability
p=0.1....
asked 51 minutes ago -
What is the vapor pressure at 20 degrees C of an ideal solution
prepared by the...
asked 48 minutes ago