Signals And Systems Quiz-1 "A"SEC [2017-18]

Random signals are non-periodic because they do not repeat in a regular pattern over time. Unlike periodic signals, which have a fixed period and can be represented by a mathematical function, random signals exhibit unpredictable variations and cannot be described by a specific mathematical formula. Therefore, it is correct to say that random signals are non-periodic.

Periodic signals are deterministic signals because they are completely predictable and repeat themselves over time. A periodic signal follows a specific pattern and can be described by a mathematical equation or formula. The signal's values at any given time can be determined precisely based on its period and amplitude. Therefore, periodic signals can be considered deterministic as their behavior is entirely known and can be determined without any uncertainty.

Time shift does not affect the amplitude of a waveform. Amplitude refers to the maximum displacement or intensity of a wave from its equilibrium position. Time shift, on the other hand, refers to a change in the position or phase of the waveform along the time axis. While time shift can alter the position of the waveform, it does not change the magnitude of the displacement or intensity, which is the amplitude. Therefore, the statement "Time shift will affect amplitude" is false.

When time scaling is applied to a signal, it stretches or compresses the time axis without changing the amplitude of the signal. This means that the magnitude or strength of the signal remains the same regardless of the time scaling factor. Therefore, it is correct to say that time scaling does not affect the amplitude of a signal.

Time shift refers to shifting a signal along the time axis, either forward or backward. This does not have any impact on the amplitude of the signal. Amplitude refers to the magnitude or strength of the signal, which remains unchanged regardless of any time shift. Therefore, the statement that time shift will not affect amplitude is true.

The convolution sum is a mathematical operation used to calculate the output of a linear time-invariant system when given an input signal. It is a fundamental tool in signal processing and is applicable to linear time-invariant systems because these systems have the property of being both linear and time-invariant. Linear means that the system obeys the principle of superposition, and time-invariant means that the system's response does not change over time. Therefore, the convolution sum can be used to analyze and predict the behavior of linear time-invariant systems.

When a wave reflects off a surface, the amplitude of the reflected wave can change. If the amplitude reflection changes sign, it means that the reflected wave is inverted or flipped compared to the original wave. This is true for certain types of waves, such as sound waves or electromagnetic waves, when they bounce off a boundary or interface.

Periodic signals are deterministic signals because they can be completely described and predicted based on their mathematical equations or formulas. These signals repeat themselves over a specific period of time, and their values at any given time can be determined precisely. In contrast, random or stochastic signals cannot be predicted or described by a mathematical equation, as they exhibit unpredictable behavior. Therefore, periodic signals are considered deterministic signals.

The correct answer is x(t) = x(t + T0). This equation represents the condition of periodicity for a continuous time signal. It states that the value of the signal x(t) at any time t is equal to the value of the signal at time t + T0, where T0 is the period of the signal. This means that the signal repeats itself after every T0 units of time.

This statement is true because the order of multiplication does not affect the result when multiplying two signals. In other words, multiplying signal x(n) by signal h(n) will give the same result as multiplying signal h(n) by signal x(n). This property is known as the commutative property of multiplication. Therefore, the given statement is true.

The statement "Amplitude reflection will not change amplitude sign" is incorrect. When a wave undergoes reflection, the amplitude sign is indeed changed. This means that if the original wave was positive, the reflected wave will be negative, and vice versa. Therefore, the correct answer is False.

The given statement is false. Convolution sum is actually used for discrete time signals, not continuous time signals. Continuous time signals are typically dealt with using convolution integrals.

Real-time instruments like oscilloscopes should be time invariant because they need to accurately measure and display signals in real-time without any distortion or time delay. Being time invariant means that the instrument's response remains consistent regardless of when the signal is measured. This is crucial for accurate analysis and troubleshooting of time-dependent signals, as any variation in the instrument's response could lead to incorrect measurements and interpretations. Therefore, real-time instruments should ideally maintain time invariance to ensure reliable and precise measurements.

Analog and digital are two distinct classifications of signals. Analog signals are continuous and can take on any value within a range, while digital signals are discrete and can only take on specific values. Therefore, analog and digital serve as examples of signal classification.

The given equation d(n-no)*d(n-mo) =d(n-(no-mo)) is not true. This is because the equation implies that the product of the differences between n and no, and n and mo, is equal to the difference between n and (no-mo). However, this is not a valid mathematical relationship. Therefore, the correct answer is False.

The correct answer is that a shift in the input signal also results in the corresponding shift in the output. This means that if the input signal is shifted to the left or right, the output signal will also be shifted in the same direction. This property is useful for analyzing and understanding the behavior of systems that involve the unit impulse function.

The statement is false because an even signal is a signal that is symmetric with respect to the y-axis, meaning that if you flip the signal horizontally, it remains unchanged. A square wave is not an example of an even signal because it is not symmetric with respect to the y-axis.

The given discrete-time signal x(n) = sin(n) is not periodic with any fundamental period. The sine function is a periodic function, but the period of sin(n) is not a constant value. The period of sin(n) depends on the value of n, and it varies as n changes. Therefore, the correct answer is "None of these" as none of the provided options correctly represents the fundamental period of the given signal.

The given equation is ax(n-no)* bd(n+n) = ab x(n). This equation is true because both sides of the equation contain the same terms, just arranged differently. The terms ax(n-no) and bd(n+n) can be simplified to axn and bdn, respectively. Therefore, the equation simplifies to axn * bdn = abxn, which is true.

All of the given options (1, 2, 3, and 4) represent stable discrete time systems. Stability in a discrete time system refers to the boundedness of the output for bounded input. In option 1, the output y(n) is obtained by scaling the input x(n) by a factor of 4, which does not affect the stability. Option 2 represents a time-reversed version of the input x(n), which also does not affect stability. Option 3 represents a scaled version of the input x(n) added to a constant value, which does not affect stability. Option 4 represents the cosine function applied to the input x(n), which is also a stable operation. Therefore, all the given options are stable discrete time systems.

A continuous system is said to be static if its output signal at any instant t depends only on the present value of the input signal and does not consider past or future values of the input. In other words, the output of a static system is determined solely by the current input and does not change with time or consider any history or future behavior of the input signal.

Periodic signals are signals that repeat themselves after a certain period of time. Trigonometric signals, such as sine and cosine waves, are examples of periodic signals. These signals can be represented mathematically using trigonometric functions. Therefore, it is correct to say that periodic signals are trigonometric signals.

The given system y(t) = x(t) + 2x(t + 3) is a causal system. In a causal system, the output at any given time depends only on the present and past values of the input. In this case, the output y(t) is a combination of the present value x(t) and the past value x(t + 3), indicating that the system is causal.

The property being described in the given answer is that when the argument of the unit impulse function δ(t) is multiplied by a constant 'a', the result is still equal to δ(t). In other words, the unit impulse function remains unchanged when its argument is scaled by a constant.

The given discrete-time signal x(n) = (-1)^n is periodic with a fundamental period of 6. This means that the signal repeats itself every 6 samples. To verify this, we can substitute different values of n into the equation and observe the pattern. For example, when n = 0, x(0) = (-1)^0 = 1. When n = 6, x(6) = (-1)^6 = 1. Similarly, when n = 12, x(12) = (-1)^12 = 1. This pattern continues, confirming that the signal repeats itself every 6 samples, thus having a fundamental period of 6.