a. Eq.1) This complex heterodyne operation shifts all the frequency components of u m (t) above 0 Hz. The DFT is an important decomposition for sequences that are finite in length. Here the sampled signal is represented as a sequence of numbers. The DFT is indeed the workhorse of modern digital signal processing, Copyright Gatestudy.com, All Rights Reserved. 0n) and sin(! These short objective type questions with answers are very important for Board exams as well as competitive exams. A is true & B is false b. 1, 2 and 3 are correct The DFT computations are greatly facilitated by fast Fourier Transform (FFT) algorithm, which reduces number of computations significantly. Such a representation is very useful for digital computations and for digital hardware implementations. Transformation from time domain to frequency domain b. Plotting of amplitude & phase spectrum c. Both a & b d. None of the above View Answer / Hide Answer A : Inverse relationship exists between the time and frequency domain representation of signal B : A signal must be necessarily limited in time as well as frequency domains. In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. a. 6. Electronics and Communication Engineering, Probability, Random Variables and Random Signals - 2 - MCQs, Probability, Random Variables and Random Signals - 1 - MCQs, Correlation and Spectral Density - MCQs with answers. a. What is/are the crucial purposes of using the Fourier Transform while analyzing any elementary signals at different frequencies? Unlike the DTFT, which is a continuous function of a continuous variable, ω, the DFT is a sequence that corresponds to samples of the DTFT. ANSWER: (a)A is true & B is false X(ejω)=11−14e−jω=11−0.25cos⁡ω+j0.25sin⁡ω ⟺X∗(ejω)=11−0.25cos⁡ω−j0.25sin⁡ω Calculating, X(ejω).X∗(ejω) =1(1−0.25cos⁡ω)2+(0.25sin⁡ω)2=11.0625−0.5cos⁡ω 12π∫−ππ11.0625−0.5cos⁡ωdω 12π∫−ππ11.0625−0.5cos⁡ωdω=16/15 We can see that, LHS = RHS.HenceProved It it does not exist say why: a) x n 0.5n u n b) x n 0.5 n c) x n 2n u n d )x n 0.5n u n e) x n 2 n A is false & B is true c. Both A & B are true d. Both A & B are false. The DFT is essentially a discrete version of the DTFT. Chapter 1 Signals 1.1 Signal Classi cations and Properties 1 1.1.1 Introduction This module will lay out some of the fundamentals of signal classi cation. Eq. Full text of "Geschichte der preußischdeutschen Unionsbestrebungen seit der Zeit Friedrich's des Großen Untertitel auf den Umschlägen Erste Abtheilung der Fürstenbund 1785.Zweite Abtheilung. ANSWER:(b) Aperiodic Discrete time signals. ANSWER: a. Discrete Time Signal should be absolutely summable. System Analysis using Fourier Series & Transform (C.T) - MCQ... Introduction to Signals and Systems - MCQs with answers, Basic Electronics Engineering - Op-amps and Applications, Analog Communication - Amplitude Modulation, Analog Communication - Pulse Analog Modulation. Home >> Category >> Electronic Engineering (MCQ) questions & answers >> Discrete Fourier Transform (DFT) 1) The filtering is performed using DFT using 1) Limited size or blocks of data 2) Small memory size 3) Large memory size 4) Large segments of data. Discrete time Fourier Transform (DFFT) of an aperiodic signal is continuous function of Ω and is periodic with period 2π. Section 5.10, The Polar Representation of Discrete-Time Fourier Transforms, pages 343-345 Section 5.11.1, Calculations of Frequency and Impulse Responses for LTI Sys-tems Characterized by Difference Equations, pages 345-347. Then ( 0) is (a) 1 4 (b) 2 (c) 4 (d) 4 3 [GATE 2005: 1 Mark] Soln. The DTFT tells us what frequency components are present X(!) All Rights Reserved. Let us now consider aperiodic signals. These short solved questions or quizzes are provided by Gkseries. It is a function of the frequency index So $(1)$ is the continuous-time representation of a sampled signal. Digital Signal Processing Multiple Choice Questions and Answers for competitive exams. This is an indirect way to produce Hilbert transforms. = X1 n=1 x[n]e j!n jX(! While the DFT could also be used for this calculation, it would only provide an equation for samples of the frequency response, not the entire curve. 3 and 4 are correct c. 1 and 2 are correct d. All the four are correct. The DTFT is often used to analyze samples of a continuous function. Exercises in Digital Signal Processing Ivan W. Selesnick January 27, 2015 Contents 1 The Discrete Fourier Transform1 2 The Fast Fourier Transform16 X x k e DTFT f : f: ¦ (1.1) Notable here are an infinite number of harmonics used in the calculation of the DTFT. tion is a Fourier series representation 7 e'j -n =T an ej[(2(QQ-i))/T]n where T = 27r and a. a. We will derive spectral representations for them just as we did for aperiodic CT signals. 3. The DTFT is a frequency-domain representation for a wide range of both finite- and infinite-length discrete-time signalsx[n]. Problems on the DTFT: Definitions and Basic Properties àProblem 3.1 Problem Using the definition determine the DTFT of the following sequences. : exp(j! Angle (phase/frequency) modulation This section does not cite any sources . = 1. Transform (DTFT) 10.1. Discrete Time Fourier Transform Definition. a. 0) !2[ ˇ;ˇ) the spectrum is zero for !6= ! Discrete-Time Fourier Transform 11-3 DISCRETE-TIME FOURIER TRANSFORM-1fX(2) ejn dU 27r 2 +00 n=-w0 x[n]
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