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Let x[n] and h[n] be two real finite-length sequences such that
We wish to compute the sequence y[n] = x[n]∗h[n], where ∗ denotes ordinary convolution.
(a) What is the length of the sequence y[n]?
(b) For direct evaluation of the convolution sum, how many real multiplications are required to compute all of the nonzero samples of y[n]? The following identity may be usefuL
(c) State a procedure for using the DFT to compute all of the nonzero samples of y[n]. Determine the minimum size of the DFTs and inverse DFTs in terms of L and P.
(d) Assume that L = P = N/2, where N = 2ν is the size of the DFT. Determine a formula for the number of real multiplications required to compute all the nonzero values of y[n] using the method of part
(c) if the DFTs are computed using a radix- 2 FFT algorithm. Use this formula to determine the minimum value of N for which the FFT method requires fewer real multiplications than the direct evaluation of the convolution sum
A 120-V source is to be connected to a load by two copper wires. The load is located 500 feet from the source. The maximum voltage drop due to the wire resistance is 10 V, which makes the minimum load voltage 110 V.
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Use decomposition to find the minimum gate input cost, multiple level implementation for the functions given, using AND, OR, NOT, XOR gates: a) F(A,B,C,D)=sigma(m)(5,6,7,9,10,11) b) G(W,X,Y,Z)=sigma(m)(5,6,7,9,10,11,14,15)
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