HW5_2005

Digital Signal Processing: A Practical Approach (2nd Edition)

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Homework Set #5: Filter Realization and Design 1. Consider a discrete-time system H ( z )= 5 4 2 1 3 2 1 4 2 3 1 3 3 4 1 + + + + + z z z z z z z , (a) Give difference equations, which characterize direct form I and draw its block diagram; (b) Give difference equations, which characterize direct form II and draw its block diagram; (c) Transposed direct form I; (d) Transposed direct form II. 2. Consider a discrete-time linear and time-invariant and causal system H ( z )= 2 1 1 2 3 1 5 . 0 1 + + z z z , (a) Draw direct form I block diagram; (b) Draw direct form II block diagram; (c) Draw parallel form ; (d) Draw cascade form. 3. A discrete-time lowpass filter is to be designed from the continuous-time Butterworth filter having magnitude-squared function: N c c j H 2 2 ) / ( 1 1 ) ( + = The specifications for the discrete-time system are π ω 35 . 0 0 1 ) ( 97250 . 0 j e H 3 0 025 . 0 ) ( . e H j Followed the design examples in any textbook, please use (a) impulse invariance method and (b) bilinear transform method to design two digital filters.
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Unformatted text preview: (i) Determine the integer order of N while using two methods. (ii) Give the transfer functions H ( z ) for these two methods. (iii) Plot their frequency responses ) ( ω j e H during π ≤ ω ≤ for these two methods. 4. If H lp ( Z ) is a given lowpass filter is transferred by Z − 1 = 1 1 25 . 1 − − − + − z z α and Z − 1 = 1 1 1 2 − − + + z z β . (a) Determine α and β such that the Z-plane to z-plane transform satisfies the transformation constraints. (b) What are the frequency responses (lowpass, bandpass or highpass) of the new transformed filters? (c) Plot the frequency transferring curves and explain their behaviors. 5. (a) Please describe the design procedures of FIR filters by using the windowing technique. (b) What are selection criteria for choosing the window function, which is the most important? Why?...
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