Consider a discrete-time system that is linear (but not necessarily time-invariant), and where: - if the...
Consider a discrete-time system that is linear (but not necessarily time-invariant), and where:
- if the input x[n] is even, then the output is y[n]= x[n-1]
- if the input x[n] is odd, then the output y[n]= x [n=1]
Find the ouput of this system if the inpus is (a) δ [n] (b) u[n]. (Do not use la place transform)
Hint: if a signal is neither even nor odd, then you can write it as a sum of an even signal and an odd signal.
Homework Answers
Add Answer to:
Consider a discrete-time system that is linear (but not
necessarily time-invariant), and where:
- if the...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
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. A discrete time system is both linear and time invariant. Suppose the output due to...
4. A discrete time system is both linear and time invariant. Suppose the output due to a unit impulse input x[n] = o[n] is h[n] as given Fig. 3a. a. Find & plot the output y[n] due to an input x[n] = 28[n] + [n-1] b. Find & plot the output y[n] due to an input In Fig. 3b. hin (a) x[n] (b) Figure 3 for Problem 4
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...
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output...
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense?...
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...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
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...
Part B, Part C and Part D...Thanks Question 1 Consider the interconnection of Linear Time-Invariant (L.TI)...
Part B, Part C and Part D...Thanks
Question 1 Consider the interconnection of Linear Time-Invariant (L.TI) system shown in Figure Q1: h2(n) Figure Ql The individual impulse responses are defined as: 1, n=0,1,2 L0, elsewhere hi (n) h2(n) (n)(u(n) -u(n 3)) h3 (n) 6(n 2) a) Define Lincar Time-Invariant (LTI) system. (3 marks) b) Determine the overall impulse response htotal (n). (12 marks) o) Determine the output y(n) if the system is excited with the following input: x(n) = δ(n...
Explain how fourier transform is done? 1. (8 points) Suppose a particular discrete-time linear and time-invariant...
Explain how fourier transform is done?
1. (8 points) Suppose a particular discrete-time linear and time-invariant (LTI) system has frequency response H(e) and that when its input is z[n] = 2 cos (n). the corresponding output is y[n] = 6 cos (n+ ) Find the real part and imaginary part of H(e)") at w = .
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
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. A discrete time system is both linear and time invariant. Suppose the output due to a unit impulse input x[n] = o[n] is h[n] as given Fig. 3a. a. Find & plot the output y[n] due to an input x[n] = 28[n] + [n-1] b. Find & plot the output y[n] due to an input In Fig. 3b. hin (a) x[n] (b) Figure 3 for Problem 4
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...
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense?...
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...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
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...
Part B, Part C and Part D...Thanks
Question 1 Consider the interconnection of Linear Time-Invariant (L.TI) system shown in Figure Q1: h2(n) Figure Ql The individual impulse responses are defined as: 1, n=0,1,2 L0, elsewhere hi (n) h2(n) (n)(u(n) -u(n 3)) h3 (n) 6(n 2) a) Define Lincar Time-Invariant (LTI) system. (3 marks) b) Determine the overall impulse response htotal (n). (12 marks) o) Determine the output y(n) if the system is excited with the following input: x(n) = δ(n...
Explain how fourier transform is done?
1. (8 points) Suppose a particular discrete-time linear and time-invariant (LTI) system has frequency response H(e) and that when its input is z[n] = 2 cos (n). the corresponding output is y[n] = 6 cos (n+ ) Find the real part and imaginary part of H(e)") at w = .
Most questions answered within 3 hours.
-
The fuel economy of a 2011 Lexus RX 350 2wd 6 cylinder 3.5 L
automatic 5...
asked 1 minute ago -
i.
the synthesized compund 2-bromo-butanal i have a IR peak at about
3200 and one at...
asked 1 minute ago -
A
752 mL sample of water was placed in a 1000 gram pan of aluminum.
The...
asked 12 minutes ago -
1.In the context of chelation, what does binding strength mean?
What happens at the molecular level...
asked 5 minutes ago -
Describe two obstacles that makes fixing atmospheric nitrogen
difficult.
asked 24 minutes ago -
Evelyn incorporates her sole proprietorship, transferring it to
newly formed Papaya Corporation. The assets transferred have...
asked 10 minutes ago -
Assume that in a hydrogen atom, the electron circles the nucleus
in a circle of radius...
asked 19 minutes ago -
1 point) Given the significance level α=0.01 find the following:
(a) left-tailed z value z= (b)...
asked 13 minutes ago -
Calculate the expected value, the variance, and the standard
deviation of the given random variable X....
asked 15 minutes ago -
T
F 53) Most differences
between human groups are the result of biology rather than
culture....
asked 28 minutes ago -
A 5.20 mW helium neon laser emits a visible laser beam with a
wavelength of 633...
asked 31 minutes ago -
Assignment:
Your
organization has made a strategic decision
to
outsourcework
currently performed in house. You have...
asked 30 minutes ago