x[n]={ 1 0<=n<=3
0 otherwise }
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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
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"
x(n) = {(1, 0≤n≤3 0, otherwise)
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)=
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
1. Find the DTFT of the sequence x[n] = 0.5%u[n] . Express the DTFT in magnitude-phase form.
solve 1-10
Explain each detail.
For each of the functions in the list below calculate two quantities fu(a)dr lim. f(x)de Function list: 1. In(x) = x" on [0, 1] n 0<x<1 6. fn(2) = 1o otherwise (0 (n+1)x - " 2. In(x) = 3 -(n+1)x + 0<r<- - sr 3 į<x< 1 + 1 + nti <r<1 * VH1 7. fn(c) = Si 0<x<n 10 otherwise 0 V 0< }<u 8. fn(x) = 1 0 3. Inc 0<< 1 otherwise...
7. Determine the DTFT of the sequence [n]-, where N is 1S 0 otherwise a positive integer. Plot it for No 4 and No 20
Problem 1 Compute graphically and plot x[n] *h[n] and x[n] *h[n] (convolutions) for (a). Find a way to derive x[n] *h[n] and x[n] * ñ[n] for (b) without any computation, by using your result of (a) and the properties of convolution. State which property you use. 0 1 2 3 4 5 6 | * 3-2-10 1 2 3 Notation: In the following problems, x[n]={a.b.c) means that_x[-1)=a, x[0]=b, x[1]=c and x[n]=0 otherwise.
5. (4 pts) Let X(ej) be the DTFT of a signal x[n] which is known to be zero for n < 0 and n > 3. We know X(eja) for four values of N as follows. X(@j0) = 10, X(eja/2) = 5 – 5j, X(ejt) = 0, X(ej37/2) = 5 + 5j (a) (3 pts) Find x[n]. (Hint: Compute the IDFT) (b) (1 pts) Find X(ej?).