4 n 1 for n 2 computation of the present value of the

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Unformatted text preview: simplicity, assume the filter to be an FIR filter of length 3 with an impulse response: h[0] = h[2] = α, h[1] = β H (e jω2 ) ≅ 0 the output reduces to y[n] ≅ A H (e jω1 ) cos(ω1n + θ(ω1) ) • Thus, the system acts like a lowpass filter • In the following example, we consider the design of a very simple digital filter 69 70 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Concept of Filtering The Concept of Filtering • The convolution sum description of this filter is then given by y[n] = h[0] x[n] + h[1] x[n − 1] + h[2] x[n − 2] = α x[n] + β x[ n − 1] + α x[n − 2] 71 • y[n] and x[n] are, respectively, the output and the input sequences • Design Objective: Choose suitable values of α and β so that the output is a sinusoidal sequence with a frequency 0.4 rad/sample Copyright © 2005, S. K. Mitra • Now, the frequency response of the FIR filter is given by H (e jω ) = h[0] + h[1] e − jω + h[2] e − j 2ω = α(1 + e − j 2ω ) + β e...
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