y[n]-5y[n-1]+6y[n-2]=2x[n]-4x[n-1] Basic Fourier Transform
The relation between input and output is from the Fourier transform of
the system given as
Find the pulse response \(h\) [n] using.
$$ y[n]-5 y[n-1]+6 y[n-2]=2 x[n]-4 x[n-1] $$
Homework Answers
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n]...
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n] = x[n] + 2x[n - 1] + x[n - 3] where x[n] is the input signal and y[n] is the output signal. a) Find H[n] the impulse response of the filter. b) Plot the impulse response c) Find the value of H( Ω) for the following values of Ω = 0, pi, pi/2, and pi/4
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x)...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x)...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) find the Fourier transform of h(t). Is this LTI system BIBO stable? Find output y(t)
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...
h(n) is a stable system, , a = 50, Find the Z-transform H(n) Find the Fourier...
h(n) is a stable system, , a = 50, Find the Z-transform H(n) Find the Fourier Transform X(n) Using MATLAB, plot the frequency response from 0 to pi and from 0 to 2pi
[b] State and prove frequency shifting property of Fourier transform Also find the fourier transform of...
[b] State and prove frequency shifting property of Fourier transform Also find the fourier transform of gate function. [c] It is given that x[0] =1, x[1]=2, x[2]=1, h[0]=1. Let y[n] be linear convolution of x[n) and h[n]. Given that y[1]=3 and y[2]-4. Find the value of the expression 10y[3]+y[4].
Use the Fourier transform to find the output y(n) when the input is x(n) = (.5)nu(n) for the following systems:
Use the Fourier transform to find the output y(n) when the input is x(n) = (.5)nu(n) for the following systems:
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 = .
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
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...
[b] State and prove frequency shifting property of Fourier transform Also find the fourier transform of gate function. [c] It is given that x[0] =1, x[1]=2, x[2]=1, h[0]=1. Let y[n] be linear convolution of x[n) and h[n]. Given that y[1]=3 and y[2]-4. Find the value of the expression 10y[3]+y[4].
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 = .
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