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Q1 Given two vectors Aln 1355715 n 122875 Arrows show the zero point. For A[n, the...
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.
MATLAB Fourier transform. Suppose that a signal x(t) is sampled with sampling frequency fs =100Hz. The sequence x[n] obtained after the sampling is given below: Take the DFT of the sampled sequence and plot its magnitude and phase. What is the frequency resolution (Δf) of your plot? N= 20, 100 Hz N= 20, 100 Hz
(b) Perform convolution to obtain the discreet if input x[n] = [1 3 2 1] and impulse response, h[n] signal output of y[n], [1 -4 2]. [3 marks] (c) An analogue signal is sampled every 50ms for a duration of 1000 seconds. i) Calculate how much data (samples) are collected. [2 marks] If a Discrete Fourier Transform (DFT) is performed what is the maximum frequency information that can be obtained? [2 marks] Calculate the minimum frequency (the frequency resolution) a...
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...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
Given two vectors A[n] = [1 355 715] B[n] = [2 2 8 75] Arrows show the zero point. For A[n], the index n = (-2,-1,0, 1, 2, 3, 4] and for B[n], the index n = (-1,0, 1, 2, 3). Calculate the C[n] = A[n] conv B [n]. Using either the numerical method or the table method. Detailed steps must be provided for full credit. Draw or plot A, B, and C.
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...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
Lab #2 Discrete-time Fourier Transform (DTFT) OBJECTIVES: • Explore the DTFT, its meanings and concepts. • Get acquainted with Matlab/Octave 1) Start MATLAB and change the “Current Directory” in the top of the window (or type) >> cd '' (example: >> cd 'C:\NIU\lab2') Alternatively, if you don't want to use MATLAB, you can open a web-browser and go to “octave-online.net”. 2) Download and execute LAB2forStudent_A.M with >> lab2forStudent_A and observe that it produces a Discrete-Time (DT) signal xVec. 3) TO...