1 LetXTk], 0sks11, be a 12-point DFT of a length-12 real-valued sequence x[n] with the first...
1. Let {X[k]}K=o be the N = 8-point DFT of the real-valued sequence x[n] = [1, 2, 3, 4]. (a) Let Y[k] = X[k]ejak + X[<k – 4 >8] be the N = 8-point DFT of a sequence y[n]. Compute y[n]. Note: Do NOT compute X[k]. (b) Let Y[k] = X*[k] be the DFT of the sequence y[n], where * denotes the conjugate. Compute the sequence y[n]. Note: Do NOT compute X[k].
Problem #5 The 4-point DFT of a certain 4-point signal, x[n], is X[k] = DFT(x[n])-[ 0 Find the signal xIn] and write in terms of delayed unit samples. Answer: X[n] = 0 12 0]
It is suggested that if you have an FFT subroutine for computing a length-N DFT, the inverse DFT of an N-point sequence X[k] can be implemented using this subroutine as follows: 1. Swap the real and imaginary parts of each DFT coefficient X[k]. 2. Apply the FFT routine to this input sequence. 3. Swap the real and imaginary parts of the output sequence. 4. Scale the resulting sequence by 1/N to obtain the sequence x[n], corresponding to the inverse DFT...
In this question, the code is need to make dft at the first and then there are many requirmentsIdentification of pole positions in a system consider the system described by the difference equationy(n) = -r2y(n – 2) + x(n)(a) Let r = 0.9 and x(n) = ?(n). Generate the output sequence y(n) for 0 ? n ? 127.Compute the N = 128 point DFT {Y(k)} and {|Y(k)|}.(b) Compute the N = 128 point DFT of the sequence?(n) = (0.92)-ny(n)Where y(n)...
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...
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given by 10 equally-spaced samples of X(e). Determine y[n]. Hint: N-point DFT of a sequence w[n] = 2-n (u[n]-u[n-N]) is W [k] = 1-22 1wk Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given...
Can you help me to solve this problem P5.30 Let X (k) be the 8-point DFT of a 3-point sequence x(n)- 15, -4,3). Let Y(k) be the 8-point DFT of a sequence y(n). Determine y(n) when Y (k) -Ws*X(-k)s. P5.30 Let X (k) be the 8-point DFT of a 3-point sequence x(n)- 15, -4,3). Let Y(k) be the 8-point DFT of a sequence y(n). Determine y(n) when Y (k) -Ws*X(-k)s.
The DFT sequence of x[n] of length x[n] is given as follows: X[0] = 2 X[1] = 2 + jα X[2] = 5-j4 X[3] = β+j3 X[k1] = 2 X[k3] = 2-j3 X[k2] = 5+j4 X[7] = γ+j3 Find α, β, γ, k1, k2 & k3
PROBLEM 1: Let xfn], O < n 3 N-1 be a length-N sequence with an N-point DFT X[k], 0 k N-1. Determine the N-point DFT's of the following length-N sequences in terms of X[k]: (a) w[n] = az[M-m1〉N] + β (n-m2)N], where m 1 and m 2 are positive integers less than N. (b) g[n] ={z[n] for n even for odd
I Need Help with 4,6,8,10,15,18 Problems 123 If f(n) is a periodic sequence with period N, it is also periodic with period 2N. Tet 8(k) denote the DFS coefficients of X(n) considered as a periodic sequence with period N and X,(k) denote the DFS coefficients of x(n) considered as a periodic sequence with period 2N. X,(k) is, of course, periodic with period N and X2(k) is periodic with period 2N. Determine 8(k) in terms of X (k). 5. Consider two...