GATE ECE 2024 | Transmission of Signal Through Discrete Time Lti Systems Question 1 | Signals and Systems

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5t) is applied to another causal and stable LTI system with impulse response h(0.5t). The resulting output is ____.

2y(0.5t)

4y(0.5t)

0.25y(2t)

0.25y(0.25t)

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

Consider a four-point moving average filter defined by the equation $$y[n] = \sum\limits_{i = 0}^3 {{\alpha _i}x[n - i]} $$. The condition on the filter coefficients that results in a null at zero frequency is

$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = - {\alpha _3}$$

$${\alpha _1} = {\alpha _2} = 1;\,{\alpha _0} = - {\alpha _3}$$

$${\alpha _0} = {\alpha _3} = 0;\,{\alpha _1} = {\alpha _2}$$

$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = {\alpha _3}$$

GATE ECE Subjects

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Network Theory

Network Elements Network Theorems Transient Response Sinusoidal Steady State Response Two Port Networks Network Graphs State Equations For Networks Miscellaneous

Control Systems

Signal Flow Graph and Block Diagram Time Response Analysis Compensators Basic of Control Systems Frequency Response Analysis Stability Root Locus Diagram State Space Analysis

Digital Circuits