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Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform ...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks]
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
ML 25 points) DTFT of a Signal Compute the discrete-time Fourier transform (DTFT) of the signal...
ML 25 points) DTFT of a Signal Compute the discrete-time Fourier transform (DTFT) of the signal x[n] = {x[0],x[1], x[2], x[3]} = {1,0,-1,0} [n] = DTFT"
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
Determine the Discrete Time Fourier Transform (DTFT) of the following discrete-time signal. x[n]=n0.1" u(n) 1-0 1e112...
Determine the Discrete Time Fourier Transform (DTFT) of the following discrete-time signal. x[n]=n0.1" u(n) 1-0 1e112 0970.1e* 5) -0.12- e in 1-0.1e) C), ei (1+0.2e-in d) =-*+0.2e-10 e / +0.2012
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of t...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
Discrete-time fourier transform
The discrete-time Fourier transform (DTFT) representation is given by: ?[?] = 1 ∫? ?(???)?????? Where 2? −? ∞?(???) = ∑ ?[?]?−????=−∞ Compute and plot the frequency spectrum of the Fourier transform for the discrete-time signal: −2 ? = −3, 1, 3?[?] = {3 ? = −4, −2, −1, 0, 2 , 4 , 50 ??ℎ??????
roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform...
roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform X(eju n-2 ). (b) Find the phase (o) of the discrete Fourier transform X
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of...
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of signal (b) Determine the signal having the following Fourier transform X(w)cos2w.
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f #...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks]
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
ML 25 points) DTFT of a Signal Compute the discrete-time Fourier transform (DTFT) of the signal x[n] = {x[0],x[1], x[2], x[3]} = {1,0,-1,0} [n] = DTFT"
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
Determine the Discrete Time Fourier Transform (DTFT) of the following discrete-time signal. x[n]=n0.1" u(n) 1-0 1e112 0970.1e* 5) -0.12- e in 1-0.1e) C), ei (1+0.2e-in d) =-*+0.2e-10 e / +0.2012
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform X(eju n-2 ). (b) Find the phase (o) of the discrete Fourier transform X
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of signal (b) Determine the signal having the following Fourier transform X(w)cos2w.
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
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