EE5410 Signal Processing
1. Consider a linear time-invariant (LTI) system with impulse response . The
discrete-time Fourier transform (DTFT) of is:
(a) Determine the transfer function and its region of convergence (ROC).
(b) Find .
2. Find the frequency response of a discrete-time stable system whose input
and output satisfy the following difference equation:
Then determine the system impulse response .
3. Figure 1 shows the block diagram representation of a causal LTI discrete-time
system with input and output .
(a) Determine the system transfer function where and
are the transforms of the input and output , respectively.
(b) Draw the block diagram representation of the system using canonic form.
(c) Is the system stable? Explain your answer.
4. Consider a causal LTI system whose system function is
Draw one signal flow graph for the system in each of the following forms:
(a) Direct form
(b) Cascade form using canonic form sections
(c) Parallel form using canonic form sections
5. Consider an ideal bandpass filter whose frequency response in is:
where and .
(a) Use the window method with rectangular window to design a causal and linearphase finite impulse response (FIR) filter of length 7 that approximates
Write down the filter transfer function with numerical values.
(b) When implementing the FIR filter with transfer function , determine the
minimum numbers of multiplications and additions for computing each output
6. Consider a causal and linear-phase FIR filter of length 3 such that
and . It is known that the magnitude of the filter frequency response
is at , while at . Determine the
values of and .
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