Problem 10: a) Given the following sequence: x[n]={1, 2, 3, 4} where x[?= 1. Use the...
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
determine and draw the signal flow graph for the N = 16 point, radix-4 decimation-in-time FFT algorithm. Using this flow graph, determine the DFT of the sequence x(n) = cos (πn/2) , 0 ≤ n ≤ 15
Problem 5 (score 30%) You are given a final sequence of N samples of a time signal sampled withk samples/sec. a) Define the Discrete Fourier-Transform (DFT) and inverse DFT of the sequence. Are there any restrictions on the samples? b) Define the z-transform of the sequence c) d) Sketch a block-diagram of a recursive, digital filter and relate the filter-coefficients to the z-transform of the sequence.
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].
For a signal x(n)=sin(2*pi*n/3) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in frequency Algorithm)
Question 3 Consider a discrete-time signal sequence given as follow: *(n) = cos ) for 0 Sns3 3 ) Calculate the 4-point Discrete Fourier Transform (DFT) of x(n). (15 marks) Calculate the radix-2 Fast Fourier Transform (FFT) for x(n). (10 marks) [Total: 25 marks) Ouestion 4 digital low-pass filter design based on an analog Chevyshev Type 1 filter requires to meet the following specifications: Passband ripple: <1dB Passband edge: 500 Hz. Stopband attenuation: > 40 dB Stopband edge: 1000 Hz...
For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm).
S For a signal x(n)=sin(2pin/3) defined for n=Oto7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm). (25 Mar
It has been shown n that the discrete Pourier transform(DFT) of a time-varying process discrete h(tk) for (k0,1,2,.. ,N - 1). is given by carry out the Cooley-Tukey formulation of FFT by following the steps below. (a) Write the expressions for DFT H, in terms of h(ta) and the inverse DFT h(tk) in terms of Hn for N =8. (b) Define W e2x/N and rewrite (a) using W. (c) Express (b) in matrix form. (d) Express n and k in...
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...