Is the system stable? Test its stability 8 8. Define DTFT pair. What are Twiddle factors of the DFT? Why need of FFT?

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Is the system stable? Test its stability 8 8. What are Twiddle factors of the DFT? Why need of FFT? Is the DFT of a finite length sequence is periodic? If so, state the reason. What is meant by radix 2 FFT? State the properties of W N k? What is bit reversal in FFT? What is the use of Fourier transform?

State and proof the properties of Fourier transform FFT: 3. Compute the DFT for the sequence. Find IDFT and sketch it. Discuss the use of FFT algorithm in linear filtering.

Define canonic and non canonic form realizations. Draw the direct form realizations of FIR systems? Mention advantages of direct form II and cascade structure?

Define Bilinear Transformation. What is prewar ping? Why is it needed? Write the expression for location of poles of normalized Butterworth filter. What is linear phase filter? What are the design techniques available for IIR filter?

What is the main drawback of impulse invariant mapping? Compare impulse invariant and bilinear transformation. Why IIR filters do not have linear phase?

Mention the properties of Butterworth filter? Mention the properties of Chebyshev filter? Why impulse invariant method is not preferred in the design of high pass IIR filter? What are Gibbs oscillations? Explain briefly Hamming window. What are the desirable properties of windowing technique? Write the equation of Bartlett window. Why FIR filters are always stable? Why rectangular window are not used in FIR filter design using window method?

What are the advantages of FIR filter? What are the advantages and disadvantages of window? What is the necessary condition and sufficient condition for the linear phase characteristic of a FIR filter? Compare Hamming and Hanning window? Why triangular window is not a good choice for designing FIR Filter? What is the advantages in linear phase realization of FIR systems?

Structures of IIR systems: 1. Explain the method of design of IIR filters using bilinear transform method. Determine H z using bilinear transformation. Convert analog filter to digital filter with cut off frequency of 0. Design a single pole low pass digital IIR filter with -3db bandwidth of 0. For the constraints 0. Determine system function H z for a Butterworth filter using Bilinear transformation.

Design a digital Butterworth filter satisfying the following specifications 0. Determine system function H z for a Butterworth filter using impulse invariant transformation. Design a digital Chebyshev low pass filter satisfying the following specifications 0.

Design a digital Butterworth High pass filter satisfying the following specifications 0. Design a realize a digital filter using bilinear transformation for the following specifications i Monotonic pass band and stop band ii Also discuss symmetric and anti symmetric cases of FIR filter.

Describe the window sequence generally used and compare the properties. Plot the magnitude and phase response. Explain the principle and procedure for designing FIR filter using rectangular window FIR structures:

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