K mitra linear convolution using dtft 1 compute the

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Unformatted text preview: tinuity of 2π at ω = 0.72 • This discontinuity can be removed using the function unwrap as indicated below Phase, radians Amplitude 1 19 DTFT Computation Using MATLAB 0 0.2 0.4 0.6 ω/π 0.8 1 -4 -2 -3 -4 -5 -6 0 0.2 0.4 0.6 0.8 Copyright/π 2005, S. K. Mitra ω© 1 -7 20 0 0.2 0.4 0.6 0.8 1 ω/π Copyright © 2005, S. K. Mitra Linear Convolution Using DTFT Linear Convolution Using DTFT • An important property of the DTFT is given by the convolution theorem in Table 3.4 • It states that if y[n] = x[n] * h[n], then the DTFT Y (e jω ) of y[n] is given by • 1) Compute the DTFTs X (e jω ) and H (e jω ) of the sequences x[n] and h[n], respectively jω jω jω • 2) Form the DTFT Y (e ) = X (e ) H (e ) jω • 3) Compute the IDFT y[n] of Y (e ) Y (e jω ) = X (e jω ) H (e jω ) • An implication of this result is that the linear convolution y[n] of the sequences x[n] and h[n] can be performed as follows: 21 x [n ] DTFT h [n ] DTFT X (e jω ) × Y ( e jω ) IDTFT y [n ] H ( e jω ) 22 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Unwrapped Phase Function The Unwrapped Phase Function 23 • For example, there is a discontinuity of 2π at ω = 0.72 in the phase response below X ( e jω ) = 1+ 2.37e − jω + 2.7e − j 2 ω +1.6 e − j 3ω + 0.41e − j 4 ω Phase Spectrum...
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This document was uploaded on 11/09/2013.

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