Question

In: Electrical Engineering

Consider the following discrete-time system: y[n] = 100 x[n] cos(0.45πn + 0.5π) (a) Determine if the...

Consider the following discrete-time system: y[n] = 100 x[n] cos(0.45πn + 0.5π)

(a) Determine if the system is linear, time-invariant, causal and stable. Justify your answers.

(b) Find the impulse response h[n] for the system and sketch the waveform.

(c) Draw the system block diagram using adder, multiplier and delay elements.

Solutions

Expert Solution


Related Solutions

Consider a discrete-time periodic signal x [ n ]   =   cos ( 0 . 7 πn ) (1)...
Consider a discrete-time periodic signal x [ n ]   =   cos ( 0 . 7 πn ) (1) Determine the fundamental period of x[n]. (2) Suppose x[n] is obtained by sampling the continuous-time signal  x ( t )   =   cos   ( πt ), by letting the sampling period to be T s =   0 . 7 and considering the sample values at each n. Is the Nyquist sampling conditions satisfied in this case? Explain and relate this to the answer given before. (3) Under that conditions would...
Use and provide Matlab for the following: Generate the discrete-time signal x[n] = 4 cos (2pi....
Use and provide Matlab for the following: Generate the discrete-time signal x[n] = 4 cos (2pi. 10. nT5) + 2cos(2pi. 100. nT5) + 3cos(2pi 200. nT's), with Ts0.001 sec. Display the signal in both time and frequency-domain. Assume that the 100 Hz component of x [n] is your desired signal while the other two components are noise. Design a suitable filter to extract the desired (i.e. 100 Hz) signal. Display the filter's response. Display the output signal in the frequency-domain....
Solve the following system : z” + y ′ = cos x, y” − z =...
Solve the following system : z” + y ′ = cos x, y” − z = sin x, z(0) = −1, z′ (0) = −1, y(0) = 1, y′ (0) = 0.
10) A continuous-time system is described by the following relation, y(t) = (cos 3t) x (t)...
10) A continuous-time system is described by the following relation, y(t) = (cos 3t) x (t) where y(t) is the output of the system and x(t) is the input to the system. D etermine by sufficient explanation whether the system is: a) Stable, b) Memoryless, c) Causal, d) Time invariant, e) Linear.
Compute the unit-­pulse response h[n] for the discrete-­time system y[n + 2] - 2y[n + 1]...
Compute the unit-­pulse response h[n] for the discrete-­time system y[n + 2] - 2y[n + 1] + y[n] = x[n] (for n = 0, 1, 2, 3)
Determine the solutions for y = y(x) for the differential  equation cos x − x sin x...
Determine the solutions for y = y(x) for the differential  equation cos x − x sin x + y 2 + 2 x y dy/dx= 0.
a. (5 Marks) 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) =...
a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?
Q1.Consider an inventory system in discrete time with the following description. At the beginning of the...
Q1.Consider an inventory system in discrete time with the following description. At the beginning of the period the inventory decreases by one unit if the inventory level at the beginning is positive other the level remains zero till the end of the period. At the end of the period nth period, the inventory is increased by an amount Vn, where {Vn|n ≥ 1} is i.i.d. with P{V1 = i} = pi , i ≥ 0. Let Xn denote the level...
Q1.Consider an inventory system in discrete time with the following description. At the beginning of the...
Q1.Consider an inventory system in discrete time with the following description. At the beginning of the period the inventory decreases by one unit if the inventory level at the beginning is positive other the level remains zero till the end of the period. At the end of the period nth period, the inventory is increased by an amount Vn, where {Vn|n ≥ 1} is i.i.d. with P{V1 = i} = pi , i ≥ 0. Let Xn denote the level...
A discrete system is described by the difference equation y(n)= 2.5y(n-1)-y(n-2)+3x(n)+3x(n-2) a. Using Z-transform, Determine all...
A discrete system is described by the difference equation y(n)= 2.5y(n-1)-y(n-2)+3x(n)+3x(n-2) a. Using Z-transform, Determine all possible impulse responses h(n) and indicate the casuality and stability properties.                                                                                                b.For the casual filter, determine the output y(n) if the input is x(n)=g(n)-2g(n-1) where g(n)=cos (pin/s)u(n).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT