Consider the convolutional encoder shown in Figure 2.
(a) Find the impulse response of the encoder
(b) Find the output codeword if the input sequence is all 1’s (1 1 1 1 1 1 . . .)
(c) Discuss the result of (b) (d) Find the polynomial representation of the encoder
(e) Sketch the state diagram of the encoder
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Consider the convolutional encoder shown in Figure 2. (a) Find the impulse response of the encode...
Consider the convolutional encoder shown in Figure 2 (a) Find the impulse response of the encoder (b) Find the output codeword if the input sequence is all 1's (111111...) (c) Discuss the result of (b) (d) Find the polynomial representation of the encoder (e) Sketch the state diagram of the encoder 2. Output input Figure 2 Consider the convolutional encoder shown in Figure 2 (a) Find the impulse response of the encoder (b) Find the output codeword if the input...
Problem 1: Consider the convolutional encoder as shown to the right. if the input bit sequence is given Input Bit (m)J U(X) g2(X) Problem 1: Consider the convolutional encoder as shown to the right. if the input bit sequence is given Input Bit (m)J U(X) g2(X)
Basic Properties of Convolutional Codes a convolutional encoder has finite memory, it can easily be represented bu m diagram. In the state-transition diagram, each state of the convolution 13.3.1 output(s) are specified. The number of lines emerging from each state is, therefoe pondi number of possible inputs to the encoder at that state, which is equal to 2. T ines merging at each state is equal to the number of states from which a tran tis represented by a box,...
For the convolutional coder circuit below compute the following: (a) Generator matrix (b) State diagram of the encoder (c) Trellis diagram of the encoder (d) Decode the received sequence 10 01 10 11 00 First coded bit Input data bits Output coded bits Second coded bit For the convolutional coder circuit below compute the following: (a) Generator matrix (b) State diagram of the encoder (c) Trellis diagram of the encoder (d) Decode the received sequence 10 01 10 11 00...
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine ??(??) and ??(??) and the ROCs B. (3 points) Using the convolutional property of the Laplace transform, determine ??(??), the Laplace transform of the output, ??(??) C. (3 points) From the answer of part B, find ??(??) 9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
2. Use a convolutional sum to find the zero-state response of an LTI system to a unit step! sequence if the system impulse response is (a) h(k)=8k), (b) h(k)= {e, k < 0 (3, k 20 3 k=o (c) h(k) = { 2 12 k=1 | 1, k=2 1o otherwise S(0.9)", k20 10, k < 0 [Ans: y(k) = 10 - 9(0.9)k, k = 0,1,2,...]
IF I b. Consider convolutional encoder with constraint length=4. The connection vectors are given by 91 = (1 110), 92 = [0 11 1) and 93 = [1 1 0 1]. i. The encoder Diagram (3 Marks) ii. State Transition Table; and (5 Marks) iii. State diagram (5 Marks)
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based on the trellis diagram of this convolutional code. (6 marks) b) Suppose that the received sequence is 1110110010. Use the Viterbi algorithm to find the most likely transmitted data sequence. (10 marks) Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based...
Create chart or table Consider the system with the impulse response ht)e u(t), as shown in Figure 3.2(a). This system's response to an input of x(t) 1) would be y(t) h(r ult 1). as shown in Figure 3.2(b). If the input signal is a sum of weighted, time-shifted impulses as described by (3.10), separated in time by Δ = 0.1 (s) so that xt)01-0.1k), as shown in Figure 3.2(c), then, according to (3.11), the output is This output signal is...
QUESTION THREE With the aid of a diagram define impulse response fully using correct 141 a) Notation 141 Find the impulse response of a discrete time accumulator b) 15) c) Derive the convolution sum esent the operations in cji) with a diagram and explain the importance of an impulse response to a discrete time L.TI system 16) in) Consider a causal L.TI discrete-time system with an impulse response h1n1-r 비nl where pct Determine the output sequence yln] 161 for a...