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This assignment was given by Dr Muhammad Faisal Butt for Digital Signal Processing course at COMSATS Institute of Information Technology, Abbottabad. Its main points are: Z-transform, Signal, Sketch, Pole-zero, Plot, Inverse, Long, Division, Partial, Fraction
Typology: Exercises
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Question no 1: Determine the Z-transform of the following signal:
Ans:
Question no 2: Determine the Z-transform of the following signals. Also, sketch the corresponding zero-pole plot:
Ans (a):
Ans (b):
Question no 3: Given the Z-transform:
Find the inverse Z-transform of the following signal using long division and partial fraction. Ans:
Question no 4: Determine the Z-transform of the following signals and sketch the ROC of the following signals
Ans (a):
Ans (b):
Question no 5: Convolve the two by means of the Z-transform
Ans:
Ans (b):
Question no 8: Consider the sampling and reconstruction system given below where x(t) is given by the formula: x(t) = 10 cos(20πt −π/4) − 5cos(50πt) a) What condition must be satisfied by the sampling rate to ensure y(t) = x(t)? b) What value of ‘fs’ should be chosen so that y(t) = A + 10 cos(20πt −π/4)? c) What is the value of the constant A? Ans:
