2. For the following signals, calculate the inverse DTFT. (n-4) (b) F3(Ω)-4 cos(2Ω)-Dj sin(312)
Find the DTFT X(Ω)of the following signals (The bold denote the index n = 0).Also,sketch the magnitude and the phase spectrum (you may use Matlab or other plotting software): 1.x[n]= {1,2,3,2,1}
2. Find the inverse DTFT of each trasform specified below, for-π < Ω < p -i, ipi < 0.2π 0, Otherwise (a) 5 points: X(Ω) (b) 5 points: X(Q)=
2 DTFT Properties (a) Use the definition of the DTFT to derive a symmetry property: if rn] is real-valued, then X(e)is conjugate symmetric about the origin. b) Use the definition of the inverse DTFT to derive a symmetry property: if X(e) is real-valued and an even function, then r[n] is real-valued and an even function, (c) Given the two sampled data signals rn] and hin], sin (즉n sin (^n) rfn] and hn Find the convolution, y[n]-Σ00-00 hkjz[n-k]. Hint: think more,...
Question 4. (20 points) Compute the DTFT of the discrete-time signals, 1) x[n] = n(0.5)"u[n]. (opt) 2) x[n] = n(0.5)”cos(4n)u[n]. (opt) 3) x[n] = (0.5)" cos(4n)u[n]. (7pt)
Find the discrete-time Fourier Series for the following periodic signals: 3. 4 cos 2.4n n + 2 sin 3.2n n x[n] a. xn 0 12 15 6 b. xn 2N No 2N C.
Problem 3.12 Find the DTFT of the following time-domain signals: (b) x[n] = alu. lal < 1 11:32 AM Wed 25 Mar '< ! Q 0 O Untitled Notebook (12) 5 * Untitled Notebook (12) W X hw3A_s2020.pdf Untitled Problem 3.14 Find the FT of the following signals: continuous la aperiodic (b) X(t) = e te n(jw) t 120
Find the inverse Fourier transform for the following signals. X(e^jw) = 2 cos(w)
2. Find the CTFT for the following PERIODIC signals: a. xdt) = sin(2t + π/4)) b. Xb(t) = 2 + cos(2π/3 t) + 4sin(5π/3 t)
Define the rectangular window as follows: wlnl otherwise (a) Show that its DTFT has the following expression: W(eju)-e-jaa, sin Me Find out what the constant α is. sin(?) (b) Make a sketch of IW(ejoj as a function of ω for the case of M-4, and show where the zero crossings are. (c) Now, consider the Hann window defined as follows, πη 2M 0, otherwise. Make a sketch of wH[n]
Define the rectangular window as follows: wlnl otherwise (a) Show that...
2. Determine the Nyquist rate for the following signals sin(4000nt) (a) x(t) = (b) x(t) = 2 + cos(1000nt) – sin(3000mt +-1 it 3 4