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Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w,...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input...
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI system for-oo < nく00.
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI...
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5)...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output...
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
(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...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the impulse response hin) l, the frequency response H(e), and the system function H(a) of this system. 10 points) (b) Write down the expressions for the magnitude |H(e)) and the angle L) of the frequeney response) Sketch |H(e) and LM(e) with respect to . 10 points (c) Is this filter low-pass, high-pass, or band-pass? Why? [5 points) (d) Given the input z[n] = 6cos (03m...
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...
Problem 3: A system has the transfer function: Gfs) -8 +24s+800 35+6 Assuming time for this system is expressed in seconds, if the system is subjected to a periodic input of 4 sin ot, determine a...
Problem 3: A system has the transfer function: Gfs) -8 +24s+800 35+6 Assuming time for this system is expressed in seconds, if the system is subjected to a periodic input of 4 sin ot, determine a) The frequency o where the amplitude of the output will be at its maximum b) The functional expression for how the output amplitude varies with-the input frequency, c) The functional expression for how the phase of the output with respect to the input varies...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI system for-oo < nく00.
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
(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...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the impulse response hin) l, the frequency response H(e), and the system function H(a) of this system. 10 points) (b) Write down the expressions for the magnitude |H(e)) and the angle L) of the frequeney response) Sketch |H(e) and LM(e) with respect to . 10 points (c) Is this filter low-pass, high-pass, or band-pass? Why? [5 points) (d) Given the input z[n] = 6cos (03m...
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...
Problem 3: A system has the transfer function: Gfs) -8 +24s+800 35+6 Assuming time for this system is expressed in seconds, if the system is subjected to a periodic input of 4 sin ot, determine a) The frequency o where the amplitude of the output will be at its maximum b) The functional expression for how the output amplitude varies with-the input frequency, c) The functional expression for how the phase of the output with respect to the input varies...
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