Will upvote! need asap. (TCO 7) Using the fundamental definition of discrete Fourier transform (DFT) x(n)e...
ASSIGNMENT 2 (C4,_CO2, PO1) 1. Calculate DFT of the following discrete-time sequence, x(n) using DFT technique x(n) = {72,-56, 159) (C4, CO2,PO1) 2. Calculate the 8-point DFT of the following discrete-time sequence, x(n) using Decimation In Time Fast Fourier transform (DIT-FFT) algorithm. Show the sketch and label all parameters on a signal flow graph/butterfly diagram structure in your answer. (1-3<ns3 x(n) = 0 elsewhere
12. Calculate the DFT of the following discrete-time signal with: x[0] = 1, x[1] = 2, x[2] =-3, x[3] = 0. The value of the DFT required for this question is X(1). (c) 4-j2, (d) not (a), not (b) and not (e). (6) 2-4, (a) 2 + j3, 13. Determine the finite length sequence, xfn] from the DFT sequence X[k]={10,15, 40,-5). Only the discrete-time signal value at x[0] is required for this question. (a) 6+j4 (b) 15, (c) 4+j4, (d)...
I need help with these problems It has been shown that the discrete Fourier transform(DFT) of a time hltk) for (k 0,1,2, N -1). is given by V-1 k--0 Choosing N8 carry out the Cooley- Tukey formulation of FFT by following the ste below (a) Write the expressions for DFT H, in terms of hita) and the inverse DFT ht) in terms of f, for N = 8. (b) Define ". ear/N and rewrite (a) using w (c) Express (b)...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
23) Show that the discrete Fourier Transform of (0,1,-1,0) is (X, X, X2,X)-10, (1-), , (1+i) 24) Find the DFT of the time sequence (2,-2), compare it's amplitude spectrum with that of (2.-2,0,0) and comment on the effect on the amplitude spectrum of adding zeros to a time sequence 25) Verify Parseval's theorem for the series (2,-2,0,0) and the shifted series (0,2.-2,0) and comment on amplitude of a shifted time series. 23) Show that the discrete Fourier Transform of (0,1,-1,0)...
A sequence has the discrete-time Fourier transform 1 - a2 X(e) ae-jw)2(1- aejw) la| < 1 (a) Find the sequence r[n] (b) Calculate X(eju)cos(w)dw/27
(TCO 4) A discrete signal or sequence is given in a table below as a function of n or a sample number. All values not shown can be assumed to be zero. Find the z-transform of the signal. Hint: Use the basic definition of z-transform: (2) => 2 (n) z ". no nor sample number Numerical value of sample or x(n) 4+3z-1 – 4z3 – 42-4 4 – 32+1 – 4z=3 – 42-4 4+3z-1 - 3z2 – 4z3 – 42-4...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
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...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...