First, digital computers are, by design, discrete-time devices, so discrete-time signals and systems includes digital computers. Sinusoidal Signal. ANSWER: (a) 1, 2 and 3 are correct i. Ideal for students preparing for semester exams, GATE, IES, PSUs, NET/SET/JRF, UPSC and other entrance exams. 1 and 2 are correct c. 1 and 3 are correct d. All the four are correct. Physical signals are usually deﬁned in continuous time, but signal processing is done more eﬃciently digitally and for discrete-time signals. 1) Samples of a continuous signal 2) A time series which is a domain of integers 3) Time series of sequence of quantities 4) Amplitude modulated wave. 3 2 1 0 21 Time (a) Find the DTFT for the signal x[n] by hand. Each value in the sequence is called a sample. (8 points) (b) In this part, you'll be comparing the DTFT that you calculated and the DFT calculated using MATLAB. Test Set - 1 - Digital Signal Processing - This test comprises 40 questions. 1, 2 and 3 are correct b. material may be reproduced, in any form or by any means, without permission in writing from the publisher. The discrete-time sinusoidal sequences may or may not be periodic. They depend on the value of ω. For a discrete time signal to be periodic, the angular frequency ω must be a rational multiple of 2π. All continuous-time signals are periodic. Impulse Response is generally denoted as h(t) or h[n]. It comes from a sampling or discretization of a continuous signal s(t) with t = n∆, where ∆ > 0 is a discrete time step known as the sampling interval. 2 Discrete Time Signals: Sampling and Transform A discrete time signal is denoted s(n) or s n, where n is an integer and the value of s can be real or complex. In other words, it is a time series that is a function over a domain of discrete integers. 2.4 c J.Fessler,May27,2004,13:10(studentversion) 2.1.2 Classication of discrete-time signals The energy of a discrete-time signal is dened as Ex 4= X1 n=1 jx[n]j2: The average power of a signal is dened as Px 4= lim N!1 1 2N +1 XN n= N jx[n]j2: If E is nite (E < 1) then x[n] is called an energy signal and P = 0. The definition of a discrete-time periodic signal is similar to that of continuous-time periodic signals, except for the fundamental period being an integer. Samples of (regularly sampled) discrete time signals, like pixels of a digital images, are sequences: they are unitless on the ordinal axis (albeit time or space), and unitless in amplitude.A sequence is. Discrete-Time System is an algorithm, which operates on a discrete time signal called an input signal according to some well-defined rules/operation. ‘Signals and systems’ is the study of systems and their interaction. 9 2011/3/2 Digital Signal Processing 17 Classification of Discrete-Time Signals Energy signals and power signals The total energy of a signal x(n) is defined by An infinite length sequence with finite sample values may or may not be an energy signal (with finite energy) The average power of a discrete-time signal x[n]is defined by Define the signal energy of x(n) over the finite interval A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. an enumerated collection of objects in which repetitions are allowed and order matters Impulse Response of a system is the reaction to any discrete time system in response to some external changes. a. 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