Using the 4-point DFT/IFFT in matrix form, determine: (a) The DFT of x[n] = [1, 2, 1, 2]. (b) The IDFT of X[k] = [0, 4, 0, 4];
Using the 4-point DFT/IFFT in matrix form, determine: (a) The DFT of x[n] = [1, 2,...
Frequency Shifting: Determine the 100-point DFT of the signal n] p[n cos(0.67 0,,2,.,99 where p[n] is the 100-point IDFT of
Frequency Shifting: Determine the 100-point DFT of the signal n] p[n cos(0.67 0,,2,.,99 where p[n] is the 100-point IDFT of
Prob.1.(6pts) Compute the 4-point i) (3pts) DFT for x(n)-l-5 4-7 -2] ii) (3pts) IDFT for X(k)-1-10 2-j6 -14 2+j6] Prob. 2. (5pts) i) (3pts)Derive the 4-point DIT (Decimation-InTime) FFT and draw its signal-flow graph representation. ii) (2pts) Using the signal-flow graph representations of the 4-point DIF FFT, calculate the 4-point DFT of X(k) for x(n)-1-5 4-7-2].
Find N-point DFT of x[n]=
n=0,1,…,N-1
X[n] =
Using the periodicity of the complex exponentials, we can write
x[n] follows:
X[n] =
The DFT coefficients are
9N/2
k=0
X[k]=
N/4
k=2 and k=-2
0
else
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]
DSP
4. (12 points) (a) (4 points) Let x[n] = {1,2, 1, 2} and h[n] = {1,-1,1, -1} be two length-4 sequences defined for 0 <n<3. Determine the circular convolution of length-4 y[n] = x[n] 4 hin). (b) (6 points) Find the 4-point discrete Fourier transform (DFT) X[k], H[k], and Y[k]. (c) (2 points) Find the 4-point inverse DFT (IDFT) of Z[k] = {X[k]H[k].
Consider the following 256-point DFT X[k]=648[k – 21] +168[k – 55] +328[k -95]+328[k – 161] +160[k – 201]+648[k – 235] for 0 <k 255. Determine the 256-point inverse DFT (IDFT) x[n] of X[k]. (Note: x[n] can be expressed as a real-valued signal/sequence.)
shown that the discrete Pourier transform(DFT) of a time-varying process h(4) for (k = 0, 1, 2, . .. ,N-1), is given by N-1 Choosing N-8 carry out the Cooley-Tukey formulation of FFT by following the steps below. (a) Write the expressions for DFT H, in terms of hite) and the inverse DFT h(te) in terms of H, for N 8 (b) Define W-ca/N and rewrite (a) using W (c) Express (b) in matrix form. (d) Express n and k...
I will upvote if u will solve
What u need?
DFT can also be obtained using matrix multiplication. Let X[r] show the transformed values and x[n] show the original signal. Using the analysis equation: Using matrix multiplication, this operation can be written as x[O X[1 1 e(2m/N) e-K4n/N) x12] [N-1]] e-j(2(N-1)T/N)e-j(4(N-1)m/N) Instead of huilt-in EFT function use matrix multinlication to solve 3th auestion [ 1 e-/(2(N-1)(N-1)T/N)]Le[N-1] DFT is an extension of DTFT in which frequency is discretized to a finite...
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].
Assuming that a 20-point DFT is computed using the prime factor
algorithm,
(a) Determine the input and output mapping tables.
(b) If the input sequence is
x[n] ={1/2, n even
{ 0, n odd
carry out the 20-point DFT of x[n] step-by-step using the prime
factor algorithm.
points) Assuming that a 20-point DFT is computed using the prime factor algorithm, a) Determine the input and output mapping tables. (b) If the input sequence is nn even 0, n odd carry...