In x[n] = sin(w*T*n), 'w' and 'T' are both constant, is the discrete-time sequence x[n] =...
2: (a) Consider a discrete-time sequence x[n] = cos(n+3). Find the fundamental period(N). (b) Consider the sinusodal signal x(t) = 10 sin(21 Fot) with analog frequency F. Write an equa- tion for the discrete time signal n. (c) In part(b) if Fe = 400Hz and the sampling frequency F. = 4kHz, determine the fundamen- tal period of x[n].
Consider the following discrete-time systems: T[x(n)] = 2x(n) T[x(n)] = 3x(n) + 4 T[x(n)] = x(n) +2x(n − 1) – x(n − 2) Use (2.12) to determine analytically to see whether these systems are time-invariant? Let x1(n) be a uniform distributed random sequence and x2(n) be a Gaussian distributed random sequence with mean 0 and variance 10 over 0 ≤ n ≤ 100. Test time-invariant of 3rd system only. Choose any values for a1 and a2.
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]...
Problem 4.8 Sketch the FT representation X6(ja) of the discrete-time signal x(n) = sin(3mm/8) assuming that (a) T- 1/2, (b) T,-3/2. See Fia 4 19 Problem 4.8 Sketch the FT representation X6(ja) of the discrete-time signal x(n) = sin(3mm/8) assuming that (a) T- 1/2, (b) T,-3/2. See Fia 4 19
5. (20points) What is the discrete time Fourier series of 2T(n-2) x = 10 sin with Mo = 12 (time period) 5. (20points) What is the discrete time Fourier series of 2T(n-2) x = 10 sin with Mo = 12 (time period)
d) Given a discrete time sequence: x[n] 218(n 2) - (n 1) +358 (n) -(n 1)218 (n - 2) where δ(n) is the unit-impulse sequence and the general Discrete Time Fourier Transform (DTFT) X(ej") is: i) ii) iii) Do the following without explicitly finding X(ejo) Determine χ[0]-4x[1] Evaluate DTFT X(ejw) at ω-0. Using one of the DTFT properties, state the value the phase value of X(eM) (ie. φ(u)) . Explain how you get the answer
/lay Figure 9.1: Discrete-time sinusoid sin 0.11 n and its Fourier spectra. x[n] = sin Olan= (010.17n – e-O.lan) (9.15) From the spectra in Fig. 9.1 write the Fourier series corresponding to the interval - 10 2r> -30 (or-T2N>-37). Show that this Fourier is equivalent to that in Eq. (9.15).
Q1. Consider the system displayed below 8[n] blul y[n] W[n] sin(in/2) where x[n] = sin(itn/4) πη w[n] = ejîn, and h[n] πη a) Sketch G(j12), the discrete-time Fourier transform of g[n], for - << +0. b) Find the output signal y[n] of the system. (10 marks) (10 marks)
ASSIGNMENT 2 (C4,_CO2, PO1) 1. Calculate DFT of the following discrete-time sequence, x(n) using DFT technique x(n) = {72,-56, 159) (C4, CO2,PO1) 2. Calculate the 8-point DFT of the following discrete-time sequence, x(n) using Decimation In Time Fast Fourier transform (DIT-FFT) algorithm. Show the sketch and label all parameters on a signal flow graph/butterfly diagram structure in your answer. (1-3<ns3 x(n) = 0 elsewhere
Let the sequence: x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0 else x[n]=0 Find with a direct calculation (without using the transformation matrix Z) the transform Z of x [n], its convergence pass, the roots (zeroes) and its poles.