signal processing
Answer questions 1β 3 for the LZD system whose initial conditions are zero, determined by the following difference equation. π¦(π)+π΄π¦(πβ1)+π΅π¦(πβ2)=π₯(π)+2π₯(πβ1)
1) If the natural response of the system is of the form π¦π(π)=πΆ1(β12β)ππ’(π)+πΆ2(13β)ππ’(π), obtain the coefficients A and B.
2) Obtain the unit impulse response of the system, h(n), using the information yd (n). Is the system (i) IIR / FIR, (ii) Stable, (iii) Causal? Please explain briefly.
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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...
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system is given by: 1+0.6z1-0.5z1 i Does...
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system is given by: 1+0.6z1-0.5z1 i Does the system have a finite impulse response (FIR) or infinite 3 impulse response (IIR)? Explain why. ii Determine the impulse response h[n] of the above system iii) Suppose that the system above was designed using the bilinear transformation method with sampling period T-0.5 s. Determine its original analogue transfer function.
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system...
please show detailed work/proof 3. The input and output of a causal LTI system satisfy the...
please show detailed work/proof
3. The input and output of a causal LTI system satisfy the following difference equation (d.e.) y[n] = ayln-1] + x[n]-a"x[n-N], N > 0 a. Determine the impulse response h[n]. Hint: solve it iteratively starting from n=0, 1, , n=N+1; x[n] = Ξ΄[n] then think what is y[n] ? b. Sketch the impulse response h[n] c. Is this an FIR or an IIR system? d. For what values of the parameter a is the system stable?
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...
Please show full Calculations for part C) 1. Consider the following causal LTI systems with difference...
Please show full Calculations for part C)
1. Consider the following causal LTI systems with difference equations (a) yIn]+3 y[n-1]+2y[n-2] - x[n] + 2xln-1] (b) y[n] +0.8 y[n-21 x[n-1]. (c) y[n] -0.5 yln-2 2x[n] -xln-21]. In each of cases a,b and c i) Find and sketch the impulse response, hin) by recursive solution. ii) Is the system FIR or IIR ? ii) Find and sketch the corresponding step response, s[n] iv) Draw the direct form & direct-form Il structures for...
Problem 1 (Marks: 2+1.5+1.5+4) A linear time-invariant system has following impulse response -(γ 0otherwise 1. Determine...
Problem 1 (Marks: 2+1.5+1.5+4) A linear time-invariant system has following impulse response -(γ 0otherwise 1. Determine if the system is stable or not. (Marks: 2) 2. Determine if the system is causal or non-causal. (Marks: 2) 3. Determine if the system is finite impulse response (FIR) or infinite impulse response (IIR). (Marks: 2) 4. If the system has input 2(n) = Ξ΄(n)-6(n-1) + Ξ΄(n-2), determine output y(n) = h(n)*2(n) for n=-1, 0, 1, 2, 3, 4, 5, 6, (Marks: 4)
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] β rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? β’ What are the initial conditions and their values for this causal and linear time-invariant system? Why? β’ Draw the block diagram of the filter relating input x[n) and output y[n] β’ Derive a formula for...
a. What is the significance of the name IIR in the IIR filter? b. How negative...
a. What is the significance of the name IIR in the IIR filter? b. How negative feedback is more stable than positive feedback? c. FIR filter described by the difference equation y(n)=x[n]+3x[n-2]+6x[n-31+ 3x [n-1] i. Find the transfer function and order of the system ii. What is the term FIR signifies? [5 Marks] A video processing system internally performs filtering operation using IIR filter defined by the transfer function 1+ 4z-1 + z-2 1- 1.52-2 -0.093752-3 Find the poles and...
please help with all parts a. b. c. d. What are the conditions on L1 and...
please help with all parts
a.
b.
c.
d.
What are the conditions on L1 and 12 so that h(I) = 1 [u(L+1) -ul- 12) represents (i) a causal system (ii) a stable system. [n] +0.15.(n-5). What is the impulse response Suppose an LTI discrete system is described by y[n] = of the system h[n]? Ans: - Given a difference equation y[n] - y(n - 1] +0.24y[n - 2) = 0.8". Obtain a solution y[n] that also satisfies y0 =...
Discrete Time Signal Processing Question 1. Consider an IIR filter A(1-2-1 cos Ο0) 1-2cos Ο02-1+2...
Discrete Time Signal Processing Question 1. Consider an IIR filter A(1-2-1 cos Ο0) 1-2cos Ο02-1+2 I. Compute its impulse response using the difference equation with an impulse signal Ξ΄(n) as the input. Use trigonometric identities to simplify the result as much as you can 2. Draw the diagram showing the implementation of this filter in terms of adders, delays and multipliers Note: The IIR filter above generates a cosinusoidal signal when an impulse signal is applied at its input.] Question...
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...
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system is given by: 1+0.6z1-0.5z1 i Does the system have a finite impulse response (FIR) or infinite 3 impulse response (IIR)? Explain why. ii Determine the impulse response h[n] of the above system iii) Suppose that the system above was designed using the bilinear transformation method with sampling period T-0.5 s. Determine its original analogue transfer function.
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system...
please show detailed work/proof
3. The input and output of a causal LTI system satisfy the following difference equation (d.e.) y[n] = ayln-1] + x[n]-a"x[n-N], N > 0 a. Determine the impulse response h[n]. Hint: solve it iteratively starting from n=0, 1, , n=N+1; x[n] = Ξ΄[n] then think what is y[n] ? b. Sketch the impulse response h[n] c. Is this an FIR or an IIR system? d. For what values of the parameter a is the system stable?
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...
Please show full Calculations for part C)
1. Consider the following causal LTI systems with difference equations (a) yIn]+3 y[n-1]+2y[n-2] - x[n] + 2xln-1] (b) y[n] +0.8 y[n-21 x[n-1]. (c) y[n] -0.5 yln-2 2x[n] -xln-21]. In each of cases a,b and c i) Find and sketch the impulse response, hin) by recursive solution. ii) Is the system FIR or IIR ? ii) Find and sketch the corresponding step response, s[n] iv) Draw the direct form & direct-form Il structures for...
Problem 1 (Marks: 2+1.5+1.5+4) A linear time-invariant system has following impulse response -(γ 0otherwise 1. Determine if the system is stable or not. (Marks: 2) 2. Determine if the system is causal or non-causal. (Marks: 2) 3. Determine if the system is finite impulse response (FIR) or infinite impulse response (IIR). (Marks: 2) 4. If the system has input 2(n) = Ξ΄(n)-6(n-1) + Ξ΄(n-2), determine output y(n) = h(n)*2(n) for n=-1, 0, 1, 2, 3, 4, 5, 6, (Marks: 4)
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] β rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? β’ What are the initial conditions and their values for this causal and linear time-invariant system? Why? β’ Draw the block diagram of the filter relating input x[n) and output y[n] β’ Derive a formula for...
a. What is the significance of the name IIR in the IIR filter? b. How negative feedback is more stable than positive feedback? c. FIR filter described by the difference equation y(n)=x[n]+3x[n-2]+6x[n-31+ 3x [n-1] i. Find the transfer function and order of the system ii. What is the term FIR signifies? [5 Marks] A video processing system internally performs filtering operation using IIR filter defined by the transfer function 1+ 4z-1 + z-2 1- 1.52-2 -0.093752-3 Find the poles and...
please help with all parts
a.
b.
c.
d.
What are the conditions on L1 and 12 so that h(I) = 1 [u(L+1) -ul- 12) represents (i) a causal system (ii) a stable system. [n] +0.15.(n-5). What is the impulse response Suppose an LTI discrete system is described by y[n] = of the system h[n]? Ans: - Given a difference equation y[n] - y(n - 1] +0.24y[n - 2) = 0.8". Obtain a solution y[n] that also satisfies y0 =...
Discrete Time Signal Processing Question 1. Consider an IIR filter A(1-2-1 cos Ο0) 1-2cos Ο02-1+2 I. Compute its impulse response using the difference equation with an impulse signal Ξ΄(n) as the input. Use trigonometric identities to simplify the result as much as you can 2. Draw the diagram showing the implementation of this filter in terms of adders, delays and multipliers Note: The IIR filter above generates a cosinusoidal signal when an impulse signal is applied at its input.] Question...
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