5. (4 pts) Let X(ej) be the DTFT of a signal x[n] which is known to...
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples from X(eu): g[n] CH 0 for n<0and n > 4 = x(e,2 ) for k = 0, 1, 2,3,4 = Find g(0] and gl1]. 12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples...
5.25 LetX(eM) denote the DTFT of the length-9 sequence x[nl=[L -3, 4. -5, 7. -5. 4, -3. II (a) For the DFT sequence X1 k obtained by sampling X(em at uniform intervals of π/6 starting from ω 0, determine the IDFT x1(n) of X1[k] without computing X) and XiK]. Can you recover x In] from xilo (b) For the DFT sequence X|k] obtained by sampling X(e,") at uniform intervals of π/4 starting from ω ะ 0 determine the IDFT x2...
Problem 3.) Find and plot X(w) and X(w), the magnitude and DTFT for the signal x[n] given by a) b) x[n]= cos(-n) x[n]-(-1)" (a)"u[n] for 0< a〈 1
1. The condition for signal x[n] to have DTFT is that x[n] is: (a) integratable, (b) differentiable, (c) summable, (d) compressible. 2. If X(92) is the DTFT of x[n], then the Fourier transform of x[-n) is (a) X(92)ej, (b) X(22)ein (c) X(32-1), (d) X(-22) 3. For 8-point computation of DFT, how many complex multiplications are involved? (a) 8, (b) 16, (c) 32, (d) 64. 4. For 32-point computation of FFT, how many complex multiplications are involved? (a) 32, (a) 325...
drcl(t,N)=sin(pi×N×t)÷(N×sin(pi×t)) 24. A signal x[n] has a DTFT, X(F) = 5 drcl(F,5). What is its signal energy?
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5. Let x(t) be a signal with x(t) = 0 for t <3. For each signal given below, determine the values of t for which it is guaranteed to be zero....
Signal xo(t) 5 cos (200π1+ 품 ) + 4 sin (300π) is sampled at a rate of Fs = 1 kHz to obtain the discrete-time signal x[n]. (a) Determine the spectrum X(ej ) of x[n] and plot its magnitude as a function of ω rad sam in tad and as a function of F in Hz. Explain whether the original signal xe(t) can be recovered from xln]. (b) Repeat part (a) for 500 Hz. (c) Repeat part (a) for 100...
Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First write the x[n] showed above as two pulse functions then take the DTFT using the equation given below Express discrete Fourier transform (DFT) of x[n] using DTFT X(Q). a. b. Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First...
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